数学标注

闫增涛

2024-10-18 40fb2059e31c525952e71782acecd97c178fb6e6

数学标注

 src/App.vue

@@ -63,6 +63,7 @@
      // artAndDance
      // artAndDrama
      // mathBook
      // civilAviation
      this.activeBook = await this.config.getBookConfig(
      process.env.VUE_APP_RESOURCE_CTX +
        (process.env.VUE_APP_ENV == "product"

 src/books/civilAviation/view/components/index.vue

@@ -54,13 +54,13 @@
      ></chapterEight> -->
      
    </div>
    <miniAudio
    <!-- <miniAudio
      :path="audioPath"
      :currentTime="currentTime"
      @closeMiniAudio="closeMiniAudio"
      ref="audioPlayer"
    >
    </miniAudio>
    </miniAudio> -->
  </div>
</template>

@@ -84,7 +84,7 @@
export default {
  data() {
    return {
      catalogLength: 9, // 总章节数
      catalogLength: 2, // 总章节数
      showCatalogList: [], // 显示的章节
      loadThreshold: 300, // 触发加载阈值
      throttleThreshold: 100, // 节流阈值
@@ -151,6 +151,7 @@
    // 默认加载章节
    this.showCatalogList = [1];
    // 滚动监听节流
    debugger
    this.throttledScrollHandler = _.throttle(
      this.scrollFun,
      this.throttleThreshold,
@@ -254,6 +255,8 @@
    // 滚动监听
    scrollFun(event) {
      // 判断向上滚动还是向下滚动
      console.log(11);
      
      if (event.target.scrollTop > this.previousScrollTop) {
        this.getAduio();
        // 向下
@@ -263,6 +266,9 @@
          currentScrollTop >=
          event.target.scrollHeight - this.loadThreshold
        ) {
          console.log(1);
          
          debugger
          // 到达阈值
          if (
            this.showCatalogList[this.showCatalogList.length - 1] <

 src/books/mathBook/assets/main.less

@@ -864,6 +864,7 @@
  .p-btn {
    display: flex;
    justify-content: left;
    align-items: center;
    flex-wrap: wrap;
    i {
      text-indent: 0;

 src/books/mathBook/view/components/chapter003.vue

@@ -124,26 +124,45 @@
          </li>
        </ul>
        <div class="padding-116">
          <p>
          <p class="p-btn" >
            <span>
              <span
                class="zt-ls"><b>例1</b></span>　我国要建设现代化产业体系，推动制造业高端化发展.李平制作了6个机械零件，它们的直径如表3-2所示.请用函数的概念描述李平制作这批机械零件的直径<i>y</i>（<i>mm</i>
              ）与零件的标号<i>x</i>的函数关系.
            </span>

            <span class="btn-box" @click="isShowAnswer0 = !isShowAnswer0">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="img">表3-2</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0082-1.jpg" /></p>
          <p><span class="zt-ls"><b>解</b></span>
          <p v-if="isShowAnswer0" >
            <span class="zt-ls"><b>解</b></span>
            设<i>x</i>表示零件的标号，<i>y</i>表示零件的直径，由表3-2，{1，2，3，4，5，6}中的任一数，<i>y</i>都有任一确定的值与它对应，所以表3-2确定了<i>y</i>与<i>x</i>的函数关系，其定义域为{1，2，3，4，5，6}，值域为{13.40，13.50，13.55，13.60，13.65，13.70}.
          </p>
          <p><span
          <p class="p-btn" >
            <span>
              <span
              class="zt-ls"><b>例2</b></span>　已知函数<i>f</i>（<i>x</i>）=3<i>x</i><sup>2</sup>-1.当自变量<i>x</i>为-1，0，1，<i>a</i>时，求它们所对应的函数值.
            </span>
            <span class="btn-box" @click="isShowAnswer1 = !isShowAnswer1">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer1" >
          <p><span class="zt-ls"><b>解</b></span> <i>f</i>（-1）=3×（-1）<sup>2</sup>-1=3-1=2，</p>
          <p>　 <i>f</i>（0）=3×0<sup>2</sup>-1=0-1=-1，</p>
          <p>　 <i>f</i>（1）=3×1<sup>2</sup>-1=3-1=2，</p>
          <p>　 <i>f</i>（<i>a</i>）=3×<i>a</i><sup>2</sup>-1=3<i>a</i><sup>2</sup>-1.</p>
          </div>    
          <div class="fieldset">
            <p><b>相关链接</b></p>
            <p class="block">魔方是由6个不同颜色的面组成的正方体，它可组成约4 325亿亿种不同颜色的组合，其最佳复原魔方颜色组合的方法是用数学方法研究出来的.</p>
@@ -159,11 +178,24 @@
          </div>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0082-2.jpg" /></p>
          <p class="img">图3-2</p>
          <p><span class="zt-ls"><b>例3</b></span>　如图3-2所示，一个边长是<i>a</i>的正方体，体积是<i>V</i>，写出体积<i>V</i> 随边长<i>a</i>
            变化的函数关系式，并指出函数的自变量和定义域.</p>
          <p>
            <span>
              <span class="zt-ls"><b>例3</b></span>　如图3-2所示，一个边长是<i>a</i>的正方体，体积是<i>V</i>，写出体积<i>V</i> 随边长<i>a</i>
              变化的函数关系式，并指出函数的自变量和定义域.
            </span>
            <span class="btn-box" @click="isShowAnswer2 = !isShowAnswer2">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer2" >
          <p><span class="zt-ls"><b>解</b></span> 体积<i>V</i> 随边长<i>a</i>变化的函数关系式是</p>
          <p class="center"><i>V</i>=<i>a</i><sup>3</sup>（<i>a</i>＞0）.</p>
          <p>其中<i>a</i>是自变量，定义域为{<i>a</i>|<i>a</i>＞0}.</p>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <examinations :cardList="questionData[78] ? questionData[78][2] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
@@ -200,9 +232,20 @@
              </mfrac>
            </math>的函数值<i>f</i>（0），因为<i>f</i>（0）无意义，因此，它的定义域是{<i>x</i>｜<i>x</i>≠0}.在实际问题中，函数的定义域通常由问题的实际背景所决定.如例3中的函数<i>V</i>=<i>a</i><sup>3</sup>，由于<i>a</i>是正方体的边长，所以函数的定义域为<i>A</i>={<i>a</i>｜<i>a</i>＞0}.
          </p>
          <p><span
          <p class="p-btn" >
            <span>
              <span
              class="zt-ls"><b>例4</b></span>　就业是最基本的民生，小凯通过自主创办奶品店实现职业发展.为促销自制酸奶，每瓶酸奶的价格是3.5元，每位顾客最多只能购买50瓶.假设某人购买这种酸奶<i>x</i>瓶，应付款<i>y</i>元.那么<i>y</i>（元）是<i>x</i>（瓶）的函数吗？如果是，请写出函数的定义域、对应关系和值域；如果不是，请说明理由.
            </span>
            <span class="btn-box" @click="isShowAnswer3 = !isShowAnswer3">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer3" >
          <p><span class="zt-ls"><b>解</b></span>
            <i>x</i>的取值范围是数集<i>A</i>={<i>x</i>|<i>x</i>≤50，<i>x</i>∈<b>N</b>}，<i>y</i>的取值范围是数集<i>B</i>={<i>y</i>|<i>y</i>=3.5<i>x</i>，<i>x</i>≤50，且<i>x</i>∈<b>N</b>}.对于集合<i>A</i>中的任一个数<i>x</i>，按照对应关系，在集合<i>B</i>中都有唯一确定的值与之对应，所以应付款<i>y</i>是购买数量<i>x</i>的函数.
          </p>
@@ -212,30 +255,31 @@
          <p>
            例4中函数的定义域为什么是{<i>x</i>|<i>x</i>≤50，<i>x</i>∈<b>N</b>}，而不是{<i>x</i>|<i>x</i>∈<b>R</b>}？这是因为此函数的定义域考虑了函数自变量取值的客观实际背景.
          </p>
          </div>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0083-2.jpg" /></p>
          <p class="img">图3-3</p>
          <p><span
          <p class="p-btn" >
            <span>
              <span
              class="zt-ls"><b>例5</b></span>　如图3-3所示，在矩形<i>ABCD</i>中，<i>AB</i>的长度是<i>x</i>（m），<i>BC</i>的长度是（12-<i>x</i>）（m），矩形<i>ABCD</i>的面积是<i>y</i>（<i>m</i><sup>2</sup>），则<i>y</i>与<i>x</i>的对应关系是<i>y</i>=<i>x</i>（12-<i>x</i>），求该函数的定义域.
            </span>
            <span class="btn-box" @click="isShowAnswer4 = !isShowAnswer4">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
            <span class="btn-box" @click="openDialog(thinkTwo)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="block"><span
              class="zt-ls2"><b>分析</b></span>　因为<i>AB</i>的长度为<i>x</i>（m），<i>BC</i>的长度为（12-<i>x</i>）（m），所以必须满足<i>x</i>＞0且12-<i>x</i>＞0才有实际意义.
          </p>
        </div>
      </div>
    </div>
    <!-- 073 -->
    <div class="page-box" page="80">
      <div v-if="showPageList.indexOf(80) > -1">
        <ul class="page-header-box">
          <li>
            <p>第三单元 函数</p>
          </li>
          <li>
            <p><span>073</span></p>
          </li>
        </ul>
        <div class="padding-116">
          <p><span class="zt-ls"><b>解</b></span> 要使函数<i>y</i>=<i>x</i>（12-<i>x</i>）有实际意义，必须满足<math display="0">
          <p v-if="isShowAnswer4" >
            <span class="zt-ls"><b>解</b></span> 要使函数<i>y</i>=<i>x</i>（12-<i>x</i>）有实际意义，必须满足<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">{</mo>
                <mtable columnspacing="1em" rowspacing="4pt">
@@ -262,8 +306,25 @@
                <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
              </mrow>
            </math>解得0＜<i>x</i>＜12.所以这个函数的定义域是{<i>x</i>|0＜<i>x</i>＜12}.</p>
        </div>
      </div>
    </div>
    <!-- 073 -->
    <div class="page-box" page="80">
      <div v-if="showPageList.indexOf(80) > -1">
        <ul class="page-header-box">
          <li>
            <p>第三单元 函数</p>
          </li>
          <li>
            <p><span>073</span></p>
          </li>
        </ul>
        <div class="padding-116">
          <p><span class="zt-ls"><b>例6</b></span>　求下列函数的定义域.</p>
          <p>（1） <math display="0">
          <p class="p-btn" >
            <span>
              （1） <math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
@@ -280,7 +341,19 @@
                  <mn>7</mn>
                </mrow>
              </mfrac>
            </math>；（2）<math display="0">
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer5 = !isShowAnswer5">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn">
            <span>
              （2）<math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
@@ -293,8 +366,19 @@
                <mo>−</mo>
                <mn>3</mn>
              </msqrt>
            </math>；</p>
          <p>（3） <math display="0">
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer6 = !isShowAnswer6">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （3） <math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
@@ -317,7 +401,17 @@
                  <mn>3</mn>
                </mrow>
              </mfrac>
            </math>.</p>
              </math>.
            </span>
            <span class="btn-box" @click="isShowAnswer7 = !isShowAnswer7">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer5" >
          <p><span class="zt-ls"><b>解</b></span>（1） 要使该函数有意义，必须满足</p>
          <p class="center">4<i>x</i>+7≠0，</p>
          <p>解得</p>
@@ -348,10 +442,14 @@
                <mo data-mjx-texclass="CLOSE">}</mo>
              </mrow>
            </math>.</p>
          </div>
          <div v-if="isShowAnswer6" >
          <p>（2） 要使该函数有意义，必须满足</p>
          <p class="center"><i>x</i>-3≥0，</p>
          <p>解得　<i>x</i>≥3.</p>
          <p>所以函数<i>f</i>（<i>x</i>）的定义域是{<i>x</i>|<i>x</i>≥3}.</p>
          </div>
          <div v-if="isShowAnswer7" >
          <p>（3） 要使该函数有意义，必须满足</p>
          <math display="block">
            <mrow data-mjx-texclass="INNER">
@@ -412,6 +510,7 @@
            </mrow>
          </math>
          <p>所以函数<i>f</i>（<i>x</i>）的定义域是{<i>x</i>|<i>x</i>≥-2且<i>x</i>≠3}.</p>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj" >
            <examinations :cardList="questionData[80]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
@@ -440,15 +539,39 @@
          <p>我们知道，上一节“观察思考”中的3个情境都涉及变量之间的函数关系.情境1中，销售收入<i>y</i>（元）与销售量<i>x</i>（kg ）的函数关系是<i>y</i>=6<i>x</i>，0≤<i>x</i>≤2
            000，这种表示函数关系的方法称为解析法；情境2中，用表格表示了发射卫星的颗数<i>y</i>与年份<i>x</i>的函数关系，这种表示函数关系的方法称为列表法；情境3中，用图像表示了气温<i>Q</i>与时间<i>t</i>的函数关系，这种表示函数关系的方法称为图像法.
          </p>
          <p><span class="zt-ls"><b>例1</b></span>　某辆汽车以30 km/<i>h</i> 的速度匀速直线行驶，用解析法表示汽车行驶的路程<i>s</i>（km
            ）与时间<i>t</i>（<i>h</i>）之间的对应关系.</p>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例1</b></span>　某辆汽车以30 km/<i>h</i> 的速度匀速直线行驶，用解析法表示汽车行驶的路程<i>s</i>（km
              ）与时间<i>t</i>（<i>h</i>）之间的对应关系.
            </span>
            <span class="btn-box" @click="isShowAnswer8 = !isShowAnswer8">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer8" >
          <p><span class="zt-ls"><b>解</b></span> 这个函数的定义域是{<i>t</i>|<i>t</i>≥0}.</p>
          <p>用解析法可将这个函数表示为<i>s</i>=30<i>t</i>，<i>t</i>≥0.</p>
          <p>用解析法表示函数关系，能够准确、完整地反映两个变量之间的关系.</p>
          <p><span class="zt-ls"><b>例2</b></span>　近年我国快递业务量迅速增长，从2017年至2021年，每年的快递业务量情况如表3-4所示（注：引自国家统计局数据）.</p>
          </div>
          <p>
            <span>
              <span class="zt-ls"><b>例2</b></span>　近年我国快递业务量迅速增长，从2017年至2021年，每年的快递业务量情况如表3-4所示（注：引自国家统计局数据）.
            </span>
            <span class="btn-box" @click="isShowAnswer9 = !isShowAnswer9">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="img">表3-4</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0087-2.jpg" /></p>
          <p>表3-4清晰地反映了年份与当年快递业务量（亿件）之间的对应关系.在实际生活中，用列表法表示变量之间对应关系的例子还有很多.例如，记录某人每天的消费情况、单位职工的每月薪资收入、银行使用的存款“利息表”等.</p>
          <p v-if="isShowAnswer9" >表3-4清晰地反映了年份与当年快递业务量（亿件）之间的对应关系.在实际生活中，用列表法表示变量之间对应关系的例子还有很多.例如，记录某人每天的消费情况、单位职工的每月薪资收入、银行使用的存款“利息表”等.</p>
        </div>
      </div>
    </div>
@@ -470,23 +593,67 @@
          </li>
        </ul>
        <div class="padding-116">
          <div v-if="isShowAnswer9" >
          <p>观察上一节“观察思考”中的情境3，我们发现用图像法表示函数关系时能直观形象地表示出函数的局部变化规律，进而可以预测它的整体变化趋势.但是我们并不能作出所有函数的图像.</p>
          </div>
          <p>
            <span>
              <span
                class="zt-ls"><b>例3</b></span>　使用环保毛巾替代一次性纸巾，是倡导低碳环保生活的一种方式.某便民超市促销某种小毛巾，每条售价4元，每人限购5条.若顾客购买<i>x</i>条小毛巾需要付款<i>y</i>元，试用图像法表示函数<i>y</i>=<i>f</i>（<i>x</i>）.
            </span>
            <span class="btn-box" @click="isShowAnswer10 = !isShowAnswer10">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer10" > 
            <p><span class="zt-ls"><b>解</b></span> 函数<i>y</i>=<i>f</i>（<i>x</i>）的定义域是{1，2，3，4，5}，用图像法可将这个函数表示为图3-4.</p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0088-1.jpg" /></p>
          <p class="img">图3-4</p>
          <p><span
              class="zt-ls"><b>例3</b></span>　使用环保毛巾替代一次性纸巾，是倡导低碳环保生活的一种方式.某便民超市促销某种小毛巾，每条售价4元，每人限购5条.若顾客购买<i>x</i>条小毛巾需要付款<i>y</i>元，试用图像法表示函数<i>y</i>=<i>f</i>（<i>x</i>）.
          </p>
          <p><span class="zt-ls"><b>解</b></span> 函数<i>y</i>=<i>f</i>（<i>x</i>）的定义域是{1，2，3，4，5}，用图像法可将这个函数表示为图3-4.</p>
          <p>
            函数的图像既可以是离散的点，也可以是线段、直线、折线、连续的曲线等.在初中，我们用列表、描点、连线的方法画出了正比例函数、反比例函数、一次函数和二次函数的图像.图像法也被大量用于各类数据统计中.例如，GDP（国内生产总值）每年的增长情况、居民消费价格每季度的增长情况、全国人口数量每年的变化情况等.
          </p>
          <p><span class="zt-ls"><b>例4</b></span>　一艘军舰与某海港相距135 n mile（1 n mile ≈1.852 km ），如果军舰以45 n mile/h 的速度向海港前行，则3
            h后可到达海港.假设这艘军舰出发t（h）后，与海港的距离是s（n mile）.</p>
          <p>（1） 用解析法表示函数<i>s</i>=<i>f</i>（<i>t</i>）；</p>
          <p>（2） 用图像法表示函数<i>s</i>=<i>f</i>（<i>t</i>）.</p>
          <p class="block"><span
              class="zt-ls2"><b>分析</b></span>　计算该军舰从出发地驶入海港所需要的时间，就可得到函数<i>s</i>=<i>f</i>（<i>t</i>）的定义域.用解析法表示函数后，再画出函数的图像.
          </div>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <p>
            <span>
              <span class="zt-ls"><b>例4</b></span>　一艘军舰与某海港相距135 n mile（1 n mile ≈1.852 km ），如果军舰以45 n mile/h 的速度向海港前行，则3
              h后可到达海港.假设这艘军舰出发t（h）后，与海港的距离是s（n mile）.
            </span>
            <span class="btn-box" @click="openDialog(thinkThree)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （1） 用解析法表示函数<i>s</i>=<i>f</i>（<i>t</i>）；
            </span>
            <span class="btn-box" @click="isShowAnswer11 = !isShowAnswer11">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（2） 用图像法表示函数<i>s</i>=<i>f</i>（<i>t</i>）.</span>
            <span class="btn-box" @click="isShowAnswer12 = !isShowAnswer12">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer11" > 
          <p><span class="zt-ls"><b>解</b></span>（1） 因为该军舰从出发地驶入海港需要用时<math display="0">
              <mfrac>
                <mn>135</mn>
@@ -497,9 +664,13 @@
              <mo>（</mo>
              <mi>h</mi>
              <mo>）</mo>
            </math>，所以函数的定义域为{<i>t</i>|0≤<i>t</i>≤3}.</p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0088-3.jpg" /></p>
          <p class="img">图3-5</p>
              </math>，所以函数的定义域为{<i>t</i>|0≤<i>t</i>≤3}.
            </p>
            <p>又因为该军舰出发<i>t</i>（<i>h</i>）后，行驶的路程为45<i>t n mile</i> ，这时该军舰与海港的距离为（135-45<i>t</i>） <i>n mile</i> .</p>
            <p>所以，用解析法可将函数<i>s</i>=<i>f</i>（<i>t</i>）表示为</p>
            <p class="center"><i>s</i>=-45<i>t</i>+135，0≤<i>t</i>≤3.</p>
          </div>

        </div>
      </div>
    </div>
@@ -512,10 +683,11 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p>又因为该军舰出发<i>t</i>（<i>h</i>）后，行驶的路程为45<i>t n mile</i> ，这时该军舰与海港的距离为（135-45<i>t</i>） <i>n mile</i> .</p>
          <p>所以，用解析法可将函数<i>s</i>=<i>f</i>（<i>t</i>）表示为</p>
          <p class="center"><i>s</i>=-45<i>t</i>+135，0≤<i>t</i>≤3.</p>
          <div v-if="isShowAnswer12" >
          <p>（2） 函数<i>s</i>=<i>f</i>（<i>t</i>）是一次函数，用图像法可将函数表示为图3-5.</p>
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0088-3.jpg" /></p>
            <p class="img">图3-5</p>
          </div>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left"><img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" /></p>
@@ -717,7 +889,18 @@
                <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
              </mrow>
            </math></p>
          <p>（1） 求<i>f</i>（-5），<i>f</i>（4）的值；</p>
          <p class="p-btn" >
            <span>
              （1） 求<i>f</i>（-5），<i>f</i>（4）的值；
            </span>
            <span class="btn-box" @click="isShowAnswer13 = !isShowAnswer13">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
        </div>
      </div>
    </div>
@@ -730,7 +913,16 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p>（2） 求<i>f</i>（<i>f</i>（-1））的值.</p>
          <p class="p-btn" >
            <span>（2） 求<i>f</i>（<i>f</i>（-1））的值.</span>
            <span class="btn-box" @click="isShowAnswer14 = !isShowAnswer14">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div class="bk">
            <div class="bj1">
              <p class="left"><img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" /></p>
@@ -739,21 +931,58 @@
              分段函数是一个函数，不能把它看成几个函数，只是在同一个函数的定义域内，不同的取值范围内对应不同的函数关系.它的定义域是各个解析式的自变量取值集合的并集，值域也是各个解析式的函数值集合的并集.它的图像也比较特殊，有时图像是不连续的.
            </p>
          </div>
          <div v-if="isShowAnswer13" >
          <p><span class="zt-ls"><b>解</b></span>（1） 因为-5＜0，所以<i>f</i>（-5）=-5+2=-3.</p>
          <p>因为4＞0，所以 <i>f</i>（4）=4<sup>2</sup>-3=13.</p>
          </div>
          <div v-if="isShowAnswer14">
          <p>（2） 因为-1＜0，所以<i>f</i>（-1）=-1+2=1.</p>
          <p>又因为1＞0，所以<i>f</i>（<i>f</i>（-1））=<i>f</i>（1）=1<sup>2</sup>-3=-2.</p>
          <p><span
          </div>
          <p>
            <span
              class="zt-ls"><b>例2</b></span>　我国是用电量最大的国家，国家发出节能减排的号召，鼓励居民节约用电，2019年国家对居民每月用电量进行划分，电价施行“分档递增”.某城市居民每月用电计费价格如表3-7所示.假设这个城市的某居民某月用电量是<i>x</i>（kW·h），需支付电费<i>y</i>（元）.
            <span class="btn-box" @click="openDialog(thinkFour)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="img">表3-7 某城市居民每月用电计费价格表</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0091-1.jpg" /></p>
          <p>（1） 用解析法表示<i>y</i>与<i>x</i>的函数关系，并画出函数的图像.</p>
          <p>（2） 如果李某家10月的用电量是180 kW·h ，那么他家应该支付电费多少？</p>
          <p>（3） 如果周某家12月支付电费294.26元，那么他家这个月的用电量是多少？</p>
          <p class="block"><span
              class="zt-ls2"><b>分析</b></span>　首先需明确这个函数的定义域.由于居民用电量不同，其收费标准也不同，所以这是分段函数.其次要厘清自变量<i>x</i>在不同的取值范围内与因变量<i>y</i>之间的对应关系，并列出相应的解析式来解决相关问题.
          <p class="p-btn" >
            <span>（1） 用解析法表示<i>y</i>与<i>x</i>的函数关系，并画出函数的图像.</span>
            <span class="btn-box" @click="isShowAnswer15 = !isShowAnswer15">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（2） 如果李某家10月的用电量是180 kW·h ，那么他家应该支付电费多少？</span>
            <span class="btn-box" @click="isShowAnswer16 = !isShowAnswer16">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（3） 如果周某家12月支付电费294.26元，那么他家这个月的用电量是多少？</span>
            <span class="btn-box" @click="isShowAnswer17 = !isShowAnswer17">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer15" >
          <p><span class="zt-ls"><b>解</b></span>（1） 函数<i>y</i>=<i>f</i>（<i>x</i>）的定义域是{<i>x</i>|<i>x</i>≥0}.</p>
          <p>当0≤<i>x</i>≤200时，<i>y</i>与<i>x</i>的对应关系是<i>y</i>=0.52<i>x</i>；</p>
          <p>当200＜<i>x</i>≤400时，<i>y</i>与<i>x</i>的对应关系是</p>
@@ -822,6 +1051,8 @@
          </math>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0092-1.jpg" /></p>
          <p class="img">图3-7</p>
            <p>这个函数的图像如图3-7所示.</p>
          </div>
        </div>
      </div>
    </div>
@@ -837,13 +1068,16 @@
          </li>
        </ul>
        <div class="padding-116">
          <p>这个函数的图像如图3-7所示.</p>
          <div v-if="isShowAnswer16" >
          <p>（2） 因为<i>x</i>=180＜200，<i>y</i>=0.52×180=93.60（元）.</p>
          <p>所以，李某家10月应该支付电费93.60元.</p>
          </div>
          <div v-if="isShowAnswer17" >
          <p>（3） 周某家电费是294.26元，由图3-7可估得<i>x</i>＞400，因此</p>
          <p class="center">0.82<i>x</i>-110=294.26，</p>
          <p>解得<i>x</i>=493.</p>
          <p>所以，周某家12月的用电量为493 kW·h .</p>
          </div>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left"><img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" /></p>
@@ -952,12 +1186,30 @@
            例如，图3-8中函数<i>y</i>=<i>x</i>是<b>R</b>上的增函数，区间（-∞，+∞）是函数<i>y</i>=<i>x</i>的增区间；函数<i>y</i>=-<i>x</i>是<b>R</b>上的减函数，区间（-∞，+∞）是函数<i>y</i>=-<i>x</i>的减区间；函数<i>y</i>=<i>x</i><sup>2</sup>在区间（-∞，0）上是减函数，在区间（0，+∞）上是增函数，区间（-∞，0）和（0，+∞）分别是函数<i>y</i>=<i>x</i><sup>2</sup>的减区间、增区间.
          </p>
          <p><span class="zt-ls"><b>例1</b></span>　图3-11是函数<i>y</i>=<i>f</i>（<i>x</i>），<i>x</i>∈［-1，8］的图像，根据图像回答下列问题.</p>
          <p>（1） 当<i>x</i>取何值时，函数值最大，最大值是多少？当<i>x</i>取何值时，函数值最小，最小值是多少？</p>
          <p>（2） 说明该函数的单调区间及在每一个区间上的单调性.</p>
          <p  class="p-btn" >
            <span>（1） 当<i>x</i>取何值时，函数值最大，最大值是多少？当<i>x</i>取何值时，函数值最小，最小值是多少？</span>
            <span class="btn-box" @click="isShowAnswer18 = !isShowAnswer18">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（2） 说明该函数的单调区间及在每一个区间上的单调性.</span>
            <span class="btn-box" @click="isShowAnswer19 = !isShowAnswer19">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0097-3.jpg" /></p>
          <p class="img">图3-11</p>
          <p><span class="zt-ls"><b>解</b></span>（1） 由图可知，当<i>x</i>=2时，函数值最大，最大值是3；当<i>x</i>=6时，函数值最小，最小值是-3.</p>
          <p>（2）
          <p v-if="isShowAnswer18" ><span class="zt-ls"><b>解</b></span>（1） 由图可知，当<i>x</i>=2时，函数值最大，最大值是3；当<i>x</i>=6时，函数值最小，最小值是-3.</p>
          <p v-if="isShowAnswer19" >（2）
            函数<i>y</i>=<i>f</i>（<i>x</i>）的单调区间有［-1，2］，［2，6］，［6，8］.函数<i>y</i>=<i>f</i>（<i>x</i>）在区间［-1，2］和［6，8］上都是增函数，在区间［2，6］上是减函数.
          </p>
        </div>
@@ -979,9 +1231,43 @@
          <p class="img">图3-12</p>
          <p><span class="zt-ls"><b>例2</b></span>　二次函数<i>f</i>（<i>x</i>）=-<i>x</i><sup>2</sup>+2<i>x</i>+3的图像如图3-12所示.
          </p>
          <p>（1） 求函数<i>f</i>（<i>x</i>）的对称轴方程、顶点坐标；</p>
          <p>（2） 找出函数<i>f</i>（<i>x</i>）的单调区间；</p>
          <p>（3） 当<i>x</i>∈［2，5］时，求函数<i>f</i>（<i>x</i>）的最大值和最小值.</p>
          <p class="p-btn" >
            <span>（1） 求函数<i>f</i>（<i>x</i>）的对称轴方程、顶点坐标；</span>
            <span class="btn-box" @click="isShowAnswer20 = !isShowAnswer20">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（2） 找出函数<i>f</i>（<i>x</i>）的单调区间；</span>
            <span class="btn-box" @click="isShowAnswer21 = !isShowAnswer21">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（3） 当<i>x</i>∈［2，5］时，求函数<i>f</i>（<i>x</i>）的最大值和最小值.</span>
            <span class="btn-box" @click="isShowAnswer22 = !isShowAnswer22">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div class="bk">
            <div class="bj1">
              <p class="left"><img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" /></p>
            </div>
            <p class="block">函数的单调性是对定义域内某个区间而言的.一个函数在其定义域上不一定具有单调性，但是在定义域内的子区间上可能具有单调性，这就是函数单调性的局部性质.</p>
          </div>
          <div v-if="isShowAnswer20" >
          <p><span class="zt-ls"><b>解</b></span>（1） 二次函数<i>y</i>=<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>的对称轴方程是<math
              display="0">
              <mi>x</mi>
@@ -1111,17 +1397,27 @@
            </mtable>
          </math>
          <p>因此，函数<i>f</i>（<i>x</i>）的对称轴方程是<i>x</i>=1，顶点坐标是（1，4）.</p>
          <div class="bk">
            <div class="bj1">
              <p class="left"><img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" /></p>
            </div>
            <p class="block">函数的单调性是对定义域内某个区间而言的.一个函数在其定义域上不一定具有单调性，但是在定义域内的子区间上可能具有单调性，这就是函数单调性的局部性质.</p>
          </div>
          <p>（2） 由图像可知，函数<i>f</i>（<i>x</i>）的增区间是（-∞，1］，减区间是［1，+∞）.</p>
          <p v-if="isShowAnswer21" >（2） 由图像可知，函数<i>f</i>（<i>x</i>）的增区间是（-∞，1］，减区间是［1，+∞）.</p>
          <div v-if="isShowAnswer22" >
          <p>（3） 因为［2，5］⫋［1，+∞），且函数在区间［1，+∞）上是减函数，所以当<i>x</i>∈［2，5］时，</p>
          <p>函数<i>f</i>（<i>x</i>）的最大值是<i>f</i>（2）=-2<sup>2</sup>+2×2+3=3，</p>
          <p>函数<i>f</i>（<i>x</i>）的最小值是<i>f</i>（5）=-5<sup>2</sup>+2×5+3=-12.</p>
          <p><span class="zt-ls"><b>例3</b></span>　判断函数<i>f</i>（<i>x</i>）=<i>x</i>+1在（-∞，+∞）上的单调性.</p>
          </div>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例3</b></span>　判断函数<i>f</i>（<i>x</i>）=<i>x</i>+1在（-∞，+∞）上的单调性.
            </span>
            <span class="btn-box" @click="isShowAnswer23 = !isShowAnswer23">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <div v-if="isShowAnswer23" >
          <p><span class="zt-ls"><b>解</b></span>
            任取<i>x</i><sub>1</sub>，<i>x</i><sub>2</sub>∈（-∞，+∞），且<i>x</i><sub>1</sub>＜<i>x</i><sub>2</sub>，那么</p>
          <p class="center">
@@ -1138,6 +1434,7 @@
            所示；当<i>k</i>＜0时，函数<i>f</i>（<i>x</i>）=<i>kx</i>+<i>b</i>在区间（-∞，+∞）上是减函数，如图3-13（2） 所示.</p>
          <p class="center"><img class="img-b" alt="" src="../../assets/images/0098-5.jpg" /></p>
          <p class="img">图3-13</p>
          </div>
        </div>
      </div>
    </div>
@@ -1315,7 +1612,9 @@
            <img class="img-c" alt="" src="../../assets/images/0102-1.jpg" style="width: 40%" />
          </p>
          <p class="img">图3-17</p>
          <p v-if="isShowExampleTwo">
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <div v-if="isShowExampleTwo">
            <p>
            <span class="zt-ls"><b>解</b></span>
            函数<i>f</i>（<i>x</i>）=|<i>x</i>|+1的定义域是（-∞，+∞），因为它是偶函数，所以根据其图像关于<i>y</i>轴对称的特点，即可画出这个函数在<i>x</i>∈（-∞，0］上的图像.
          </p>
@@ -1326,6 +1625,7 @@
            <img class="img-c" alt="" src="../../assets/images/0102-2.jpg" style="width: 40%" />
          </p>
          <p class="img">图3-18</p>
          </div>
          <div class="bk">
            <div class="bj1">
              <p class="left">
@@ -1349,24 +1649,11 @@
                    transform="translate(-3327.144 15329)" />
                </svg>
              </span>
              <span class="btn-box" @click="openThinkingDialog">
              <span class="btn-box" @click="openDialog(thinkOne)">
                <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                  <path class="a"
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                <svg xmlns="http://www.w3.org/2000/svg" width="15.28" height="17.563" viewBox="0 0 19.28 20.563">
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                    <path class="a"
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                      transform="translate(-3316.14 15289.201)" />
                    <path class="a"
                      d="M316.806,239.727a.6.6,0,1,0,.6-.6A.6.6,0,0,0,316.806,239.727Zm-5.421-4.207a.6.6,0,1,0,.6.6A.587.587,0,0,0,311.385,235.52Zm2.4,8.438a.607.607,0,1,0-.6-.613A.621.621,0,0,0,313.789,243.958Z"
                      transform="translate(-196.896 -148.921)" />
                    <path class="a" d="M763.392,793.79l3.262-3.262h-3.262Z" transform="translate(-638.661 -690.634)" />
                  </g>
                </svg>
              </span>
              <span class="btn-box" @click="openMathDiaolog">
@@ -1566,10 +1853,21 @@
          <p>我们也可以由函数图像是否关于原点中心对称来判断函数是不是奇函数.</p>
          <p class="center"><img class="img-f" alt="" src="../../assets/images/0105-1.jpg" /></p>
          <p class="img">图3-20</p>
          <p><span class="zt-ls"><b>例4</b></span>　根据图3-21中函数的图像，判断哪些函数是奇函数.</p>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例4</b></span>　根据图3-21中函数的图像，判断哪些函数是奇函数.
            </span>
            <span class="btn-box" @click="isShowAnswer24 = !isShowAnswer24">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="center"><img class="img-b" alt="" src="../../assets/images/0105-2.jpg" /></p>
          <p class="img">图3-21</p>
          <p><span class="zt-ls"><b>解</b></span> 在四个函数图像中，图3-21（1） 、图3-21（2） 和图3-21（3） 的函数图像关于原点中心对称；图3-21（4）
          <p v-if="isShowAnswer24" ><span class="zt-ls"><b>解</b></span> 在四个函数图像中，图3-21（1） 、图3-21（2） 和图3-21（3） 的函数图像关于原点中心对称；图3-21（4）
            的函数图像不是关于原点中心对称的.根据奇函数的图像具有关于原点中心对称的特点，图3-21（1） 、图3-21（2） 和图3-21（3） 的函数是奇函数，图3-21（4） 的函数不是奇函数.</p>
        </div>
      </div>
@@ -1586,7 +1884,9 @@
          </li>
        </ul>
        <div class="padding-116">
          <p><span class="zt-ls"><b>例5</b></span>　已知函数<math display="0">
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例5</b></span>　已知函数<math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
@@ -1598,7 +1898,20 @@
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
            </math>图像在<i>y</i>轴右边的部分如图3-22所示.试画出这个函数图像在<i>y</i>轴左边的部分.</p>
              </math>图像在<i>y</i>轴右边的部分如图3-22所示.试画出这个函数图像在<i>y</i>轴左边的部分.
            </span>
            <span class="btn-box" @click="isShowAnswer25 = !isShowAnswer25">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0106-3.jpg" /></p>
          <p class="img">图3-22</p>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <div v-if="isShowAnswer25" >
          <p><span class="zt-ls"><b>解</b></span> 函数<math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
@@ -1615,13 +1928,24 @@
          <p>
            如图3-23所示，在<i>y</i>轴右边的图像上取三个不同点<i>A</i>，<i>B</i>和<i>C</i>，并画出它们分别关于原点对称的点<i>A</i>′，<i>B</i>′和<i>C</i>′，然后按相同方式用光滑的曲线连线，就得到这个函数的图像在<i>y</i>轴左边的部分.
          </p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0106-3.jpg" /></p>
          <p class="img">图3-22</p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0106-4.jpg" /></p>
          <p class="img">图3-23</p>
          <p>与偶函数的判定方法类似，除了借助函数的图像来判断函数是不是奇函数，也可用定义判断函数是不是奇函数.</p>
          </div>
          <p><span class="zt-ls"><b>例6</b></span>　判断下列函数是不是奇函数.</p>
          <p>（1） <i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>；（2） <math display="0">
          <p class="p-btn" >
            <span>（1） <i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>；</span>
            <span class="btn-box" @click="isShowAnswer26 = !isShowAnswer26">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2） <math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
@@ -1635,7 +1959,27 @@
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
            </math>；（3） <i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|.</p>
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer27 = !isShowAnswer27">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（3） <i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|.</span>
            <span class="btn-box" @click="isShowAnswer28 = !isShowAnswer28">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer26" >
          <p><span class="zt-ls"><b>解</b></span>（1）
            函数<i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，且
          </p>
@@ -1643,6 +1987,8 @@
            <i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>3</sup>+（-<i>x</i>）=-<i>x</i><sup>3</sup>-<i>x</i>=-（<i>x</i><sup>3</sup>+<i>x</i>）=-<i>f</i>（<i>x</i>）.
          </p>
          <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>是奇函数.</p>
          </div>
          <div v-if="isShowAnswer27" >
          <p>（2）
            要使函数<i>f</i>（<i>x</i>）有意义，必须满足<i>x</i>≠0，所以函数<i>f</i>（<i>x</i>）的定义域是<i>D</i>={<i>x</i>|<i>x</i>≠0}，对任意<i>x</i>∈<i>D</i>，都有-<i>x</i>∈<i>D</i>，且
          </p>
@@ -1702,8 +2048,16 @@
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
            </math>是奇函数.</p>
              </math>是奇函数.
            </p>
          </div>
          <div v-if="isShowAnswer28"  >
          <p>（3） 函数<i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，但是</p>
            <p class="center">
              <i>f</i>（-<i>x</i>）=（-<i>x</i>）+|-<i>x</i>|=-<i>x</i>+|<i>x</i>|=-（<i>x</i>-|<i>x</i>|）≠-<i>f</i>（<i>x</i>）.
            </p>
            <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|不是奇函数.</p>
          </div>
        </div>
      </div>
    </div>
@@ -1716,10 +2070,6 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p class="center">
            <i>f</i>（-<i>x</i>）=（-<i>x</i>）+|-<i>x</i>|=-<i>x</i>+|<i>x</i>|=-（<i>x</i>-|<i>x</i>|）≠-<i>f</i>（<i>x</i>）.
          </p>
          <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|不是奇函数.</p>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
@@ -1731,7 +2081,19 @@
          </div>
          <p>如果一个函数是奇函数或偶函数，那么就称这个函数具有<b>奇偶性</b>.否则，函数不具有奇偶性.</p>
          <p><span class="zt-ls"><b>例7</b></span>　判断下列函数的奇偶性.</p>
          <p>（1） <i>f</i>（<i>x</i>）=<i>x</i><sup>4</sup>；（2） <math display="0">
          <p class="p-btn" >
            <span>（1） <i>f</i>（<i>x</i>）=<i>x</i><sup>4</sup>；</span>
            <span class="btn-box" @click="isShowAnswer29 = !isShowAnswer29">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn">
            <span>
              （2） <math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
@@ -1746,8 +2108,31 @@
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
            </math>；</p>
          <p>（3） <i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>；（4）<math display="0">
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer30 = !isShowAnswer30">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn">
            <span>
              （3） <i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>；
            </span>
            <span class="btn-box" @click="isShowAnswer31 = !isShowAnswer31">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （4）<math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
@@ -1763,12 +2148,24 @@
                  <mn>1</mn>
                </mrow>
              </mfrac>
            </math>.</p>
              </math>.
            </span>
            <span class="btn-box" @click="isShowAnswer32 = !isShowAnswer32">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer29" >
          <p><span class="zt-ls"><b>解</b></span>（1）
            <i>f</i>（<i>x</i>）的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，且
          </p>
          <p class="center"><i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>4</sup>=<i>x</i><sup>4</sup>=<i>f</i>（<i>x</i>），</p>
          <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>4</sup>是偶函数.</p>
          </div>
          <div v-if="isShowAnswer30" >
          <p>（2）
            要使函数<i>f</i>（<i>x</i>）有意义，必须满足<i>x</i>≠0，所以函数<i>f</i>（<i>x</i>）的定义域是<i>D</i>={<i>x</i>|<i>x</i>≠0}，对任意<i>x</i>∈<i>D</i>，都有-<i>x</i>∈<i>D</i>，
            且</p>
@@ -1831,13 +2228,19 @@
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
            </math>是奇函数.</p>
              </math>是奇函数.
            </p>

          </div>
          <div v-if="isShowAnswer31" >
          <p>（3）
            函数<i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，且
          </p>
          <p class="center"><i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>2</sup>+（-<i>x</i>）=<i>x</i><sup>2</sup>-<i>x</i>，</p>
          <p>但　<i>f</i>（-<i>x</i>）≠<i>f</i>（<i>x</i>），且<i>f</i>（-<i>x</i>）≠-<i>f</i>（<i>x</i>），</p>
          <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>既不是奇函数，也不是偶函数.</p>
          </div>
          <div v-if="isShowAnswer32" >
          <p>（4）
            要使函数<i>f</i>（<i>x</i>）有意义，必须满足<i>x</i>-1≠0，所以函数<i>f</i>（<i>x</i>）的定义域是<i>D</i>={<i>x</i>|<i>x</i>≠1}，对任意<i>x</i>∈<i>D</i>，不都有-<i>x</i>∈<i>D</i>成立.
          </p>
@@ -1857,7 +2260,9 @@
                  <mn>1</mn>
                </mrow>
              </mfrac>
            </math>不具有奇偶性，它既不是奇函数也不是偶函数.</p>
              </math>不具有奇偶性，它既不是奇函数也不是偶函数.
            </p>
          </div>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left"><img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" /></p>
@@ -1926,14 +2331,54 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p><span class="zt-ls"><b>例1</b></span>　住在A城的小李早晨8：00出发，驾驶小轿车从A城以80 km/h 的速度到200 km处的B城，他在B城停留了3 h 后，再以100
            km/h的速度返回A城.在不考虑堵车等其他因素的情况下，设小李从A城出发<i>x</i>（h）后，小李与A城的距离是<i>y</i>（km）.</p>
          <p>（1） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）；</p>
          <p>（2） 画出函数<i>y</i>=<i>f</i>（<i>x</i>）的图像；</p>
          <p>（3） 小李在返回A城途中，15：00刚好接到家人的电话，这时他距离A城多少千米？</p>
          <p class="block"><span
              class="zt-ls2"><b>分析</b></span>　首先求出小李从A城到B城和从B城返回A城共花费的时间，明确函数的定义域.小李去B城和返回A城的过程中，<i>y</i>与<i>x</i>分别对应的解析式不相同，所以该函数需用分段函数表示.
          <p>
            <span>
              <span class="zt-ls">
              <b>例1</b></span>　住在A城的小李早晨8：00出发，驾驶小轿车从A城以80 km/h 的速度到200 km处的B城，他在B城停留了3 h 后，再以100
              km/h的速度返回A城.在不考虑堵车等其他因素的情况下，设小李从A城出发<i>x</i>（h）后，小李与A城的距离是<i>y</i>（km）.
            </span>
            <span class="btn-box" @click="openDialog(thinkFive)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （1） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）；
            </span>
            <span class="btn-box" @click="isShowAnswer33 = !isShowAnswer33">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（2） 画出函数<i>y</i>=<i>f</i>（<i>x</i>）的图像；</span>
            <span class="btn-box" @click="isShowAnswer34 = !isShowAnswer34">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <p class="p-btn" >
            <span>（3） 小李在返回A城途中，15：00刚好接到家人的电话，这时他距离A城多少千米？</span>
            <span class="btn-box" @click="isShowAnswer35 = !isShowAnswer35">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer33" >
          <p><span class="zt-ls"><b>解</b></span>（1） 小李从A城出发到B 城用时<math display="0">
              <mfrac>
                <mn>200</mn>
@@ -2014,13 +2459,19 @@
                </mtable>
                <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
              </mrow>
            </math>.</p>
              </math>.
            </p>
          </div>
          <div v-if="isShowAnswer34">
          <p>（2） 函数<i>y</i>=<i>f</i>（<i>x</i>）的图像如图3-24所示.</p>
          <p class="center"><img class="img-f" alt="" src="../../assets/images/0111-4.jpg" /></p>
          <p class="img">图3-24</p>
          </div>
          <div v-if="isShowAnswer35" >
          <p>（3） 小李从早晨8：00出发到15：00，共经过了7h，所以<i>x</i>=7，由（1） 中解析式得小李与<i>A</i>城的距离为</p>
          <p class="center">-100×7+750=50（km）.</p>
          <p>所以，小李返回A城途中接到家人电话时，距离A城刚好50 km.</p>
          </div>
        </div>
      </div>
    </div>
@@ -2036,13 +2487,29 @@
          </li>
        </ul>
        <div class="padding-116">
          <p><span class="zt-ls"><b>例2</b></span>　某农户要用6 000块砖建造三间面积相等的饲养室，如图3-25所示，其中<i>AB</i>，<i>AD</i>两面靠墙，每修筑长度1
            m的新墙需要砖200块.当<i>AB</i>为多少米时，修建的三间饲养室的总面积最大？最大面积是多少？</p>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例2</b></span>　某农户要用6 000块砖建造三间面积相等的饲养室，如图3-25所示，其中<i>AB</i>，<i>AD</i>两面靠墙，每修筑长度1
              m的新墙需要砖200块.当<i>AB</i>为多少米时，修建的三间饲养室的总面积最大？最大面积是多少？
            </span>
            <span class="btn-box" @click="openDialog(thinkSix)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
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                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
            <span class="btn-box" @click="isShowAnswer36 = !isShowAnswer36">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="center"><img class="img-f" alt="" src="../../assets/images/0112-1.jpg" /></p>
          <p class="img">图3-25</p>
          <p class="block"><span
              class="zt-ls2"><b>分析</b></span>　首先需要计算备用材料可修建饲养室新墙的总长；因每间饲养室的周长是定值，所以设<i>AB</i>的长为<i>x</i>（m），就可以用含<i>x</i>的代数式表示<i>BC</i>的长；再用解析法表示总面积<i>y</i>（m<sup>2</sup>）与<i>x</i>（m）的函数关系；然后利用函数的性质来解决问题.
          </p>
          <div v-if="isShowAnswer36" > 
          <p><span class="zt-ls"><b>解</b></span> 因为每修筑长度1 m的新墙需要砖200块，所以6 000块砖可以修筑新墙的总长度是6
            000÷200=30（m）.设<i>AB</i>为<i>x</i>（m），则<i>BC</i>为（30-3<i>x</i>）（m），三间饲养室的总面积为<i>y</i>（m<sup>2</sup>）.</p>
          <p>于是<i>y</i>=（30-3<i>x</i>）<i>x</i>，要有实际意义，必须满足<math display="0">
@@ -2078,29 +2545,58 @@
          <p>所以，当<i>x</i>=5时，<i>y</i>值最大，最大值为75.</p>
          <p>即当<i>AB</i>为5 m时，三间饲养室的总面积最大，最大面积是75 m<sup>2</sup>.</p>
          <p>在实际生活中，很多与二次函数有关的最值问题都可通过分析、研究后，建立相应二次函数的数学模型，并运用二次函数的图像性质求最值.</p>
          <p><span class="zt-ls"><b>例3</b></span>　某批发商购入一批30元/kg的绿色食品，若以40元/kg销售，则每月可批发销售400
          </div>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例3</b></span>　某批发商购入一批30元/kg的绿色食品，若以40元/kg销售，则每月可批发销售400
            kg.由批发销售经验知道，每月销售量<i>y</i>（kg
            ）是销售单价<i>x</i>（元）的一次函数，其图像如图3-26所示.</p>
              ）是销售单价<i>x</i>（元）的一次函数，其图像如图3-26所示.
            </span>
            <span class="btn-box" @click="openDialog(thinkSeven)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
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                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0112-3.jpg" /></p>
          <p class="img"> 图3-26</p>
          <p>（1） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）；</p>
          <p>（2） 该批发商不低于购入价进行销售，设该批发商每月销售这批绿色食品可获得利润为<i>w</i>元，用解析法表示函数<i>w</i>=<i>g</i>（<i>x</i>）；</p>
          <p>（3） 当销售单价为多少时，该批发商每月可获得最大利润？最大利润是多少？</p>
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        <ul class="page-header-odd fl al-end">
          <li>102-103</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p class="block"><span
              class="zt-ls2"><b>分析</b></span>　先由图像求出一次函数的解析式，再根据每月所获利润=（销售单价-进价）×每月销售量，列出每月所获利润<i>w</i>与销售单价<i>x</i>的函数关系.
          <p class="p-btn">
            <span>（1） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）；</span>
            <span class="btn-box" @click="isShowAnswer38 = !isShowAnswer38">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn">
            <span>
            （2） 该批发商不低于购入价进行销售，设该批发商每月销售这批绿色食品可获得利润为<i>w</i>元，用解析法表示函数<i>w</i>=<i>g</i>（<i>x</i>）；
            </span>
            <span class="btn-box" @click="isShowAnswer39 = !isShowAnswer39">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn">
            <span>
            （3） 当销售单价为多少时，该批发商每月可获得最大利润？最大利润是多少？
            </span>
            <span class="btn-box" @click="isShowAnswer40 = !isShowAnswer40">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer38" > 
          <p><span class="zt-ls"><b>解</b></span>（1） 设函数<i>y</i>=<i>f</i>（<i>x</i>）的解析式是<i>y</i>=<i>kx</i>+<i>b</i>，则</p>
          <p><math display="0">
              <mrow data-mjx-texclass="INNER">
@@ -2163,15 +2659,32 @@
          <p>根据题意，当30≤<i>x</i>≤60时，函数<i>y</i>=-20<i>x</i>+1 200才有实际意义.</p>
          <p>所以，函数<i>y</i>=<i>f</i>（<i>x</i>）的解析式可表示为</p>
          <p class="center"><i>y</i>=-20<i>x</i>+1 200，30≤<i>x</i>≤60.</p>
          </div>
          <div v-if="isShowAnswer39" > 
          <p>（2） 由题意得，<i>w</i>=（<i>x</i>-30）<i>y</i></p>
          <p>　　　　　　　　=（<i>x</i>-30）（-20<i>x</i>+1 200）</p>
          <p>　　　　　　　　=-20<i>x</i><sup>2</sup>+1 800<i>x</i>-36 000，</p>
          <p>所以，函数<i>w</i>=<i>g</i>（<i>x</i>）的解析式可表示为</p>
          <p class="center"><i>w</i>=-20<i>x</i><sup>2</sup>+1 800<i>x</i>-36 000，30≤<i>x</i>≤60.</p>
          </div>
          <div v-if="isShowAnswer40" > 
          <p>（3） 由（2） 知，<i>w</i>=-20<i>x</i><sup>2</sup>+1 800<i>x</i>-36 000，30≤<i>x</i>≤60，配方得</p>
          <p class="center"><i>w</i>=-20（<i>x</i>-45）<sup>2</sup>+4 500.</p>
          <p>所以，当<i>x</i>=45时，<i>w</i>的值最大，最大值是4 500.</p>
          <p>答：当销售单价为45元时，该批发商每月可获得最大利润，最大利润是4 500元.</p>
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          <li>上册</li>
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            <examinations :cardList="questionData[110]" :hideCollect="true" sourceType="json"
@@ -2330,9 +2843,11 @@
      <iframe src="https://www.geogebra.org/calculator" frameborder="0" style="width: 100%; min-height: 800px"></iframe>
    </el-dialog>
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      <div slot="title" style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
        <span style=""> 解题思路 </span>
    <el-dialog :visible.sync="thinkingDialog" width="40%" :append-to-body="true" :show-close="false"
      @close="closeDialog" class="thinkDialog">
      <div slot="title" class="think-header"
        style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
        <span style=""> 分析 </span>
        <svg style="position: absolute; right:10px;cursor: pointer;" @click="thinkingDialog = false" t="1718596022986"
          class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
          height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
@@ -2345,8 +2860,8 @@
        </svg>
      </div>
      <ul>
        <li v-for="(item, index) in thinkOne" :key="index">
          <div v-if="item.isShow" style="display: flex">
        <li v-for="(item, index) in thinkData" :key="index">
          <div v-if="index <= showIndex" style="display: flex">
            <span style="position: relative">
              <span style="position: absolute; top: 16px; left: 13px; color: #fff">{{ index + 1 }}</span>
              <img src="../../assets/images/icon/blue-group.png" alt="" style="margin-right: 10px"
@@ -2354,67 +2869,17 @@
              <img src="../../assets/images/icon/blue.png" alt="" v-if="index == thinkOne.length - 1"
                style="margin-right: 10px" />
            </span>
            <p class="txt-p">{{ item.txt }}</p>
            <p class="txt-p" v-html="item"></p>
          </div>
        </li>
      </ul>
      <div @click="showNext(thinkIndex)" style="
      <div @click="changeNext" style="
          display: flex;
          flex-direction: column;
          align-items: center;
          justify-content: center;
        ">
        <img src="../../assets/images/icon/mouse.png" alt="" v-if="thinkIndex != 3" />
        <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" t="1710234570135"
          class="icon" viewBox="0 0 1024 1024" version="1.1" p-id="5067" width="15" height="15">
          <path
            d="M2.257993 493.371555 415.470783 906.584344 512 1003.113561 608.529217 906.584344 1021.742007 493.371555 925.212789 396.842337 512 810.055127 98.787211 396.842337Z"
            fill="#1296db" p-id="5068" />
          <path
            d="M2.257993 117.980154 415.470783 531.192944 512 627.722161 608.529217 531.192944 1021.742007 117.980154 925.212789 21.450937 512 434.663727 98.787211 21.450937Z"
            fill="#1296db" p-id="5069" />
        </svg>
      </div>
    </el-dialog>
    <!-- 解题步骤弹窗 -->
    <el-dialog class="stepDialog" title="解题步骤" :visible.sync="stepDialog" width="40%" :append-to-body="true"
      :show-close="false">
      <div slot="title" style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
        <span>
          解题步骤
        </span>
        <svg style="position: absolute; right:10px;cursor: pointer;" @click="stepDialog = false" t="1718596022986"
          class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
          height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
          <path
            d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
            fill="#979797" p-id="4253"></path>
          <path
            d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
            fill="#979797" p-id="4254"></path>
        </svg>
      </div>
      <ul>
        <li v-for="(item, index) in stepOne" :key="index">
          <div v-if="item.isShow" style="display: flex">
            <span style="position: relative">
              <span style="position: absolute; top: 16px; left: 13px; color: #fff">{{ index + 1 }}</span>
              <img src="../../assets/images/icon/blue-group.png" alt="" style="margin-right: 10px"
                v-if="index < stepOne.length - 1" />
              <img src="../../assets/images/icon/blue.png" alt="" v-if="index == stepOne.length - 1"
                style="margin-right: 10px" />
            </span>
            <p class="txt-p">{{ item.txt }}</p>
          </div>
        </li>
      </ul>
      <div @click="showNextChange(stepIndex)" style="
          display: flex;
          flex-direction: column;
          align-items: center;
          justify-content: center;
        ">
        <img src="../../assets/images/icon/mouse.png" alt="" v-if="stepIndex != 2" />
        <img src="../../assets/images/icon/mouse.png" alt="" v-if="showIndex < thinkData.length - 1" />
        <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" t="1710234570135"
          class="icon" viewBox="0 0 1024 1024" version="1.1" p-id="5067" width="15" height="15">
          <path
@@ -2441,7 +2906,7 @@
  }
  return obj
}
const showObj = handleShow(30)
const showObj = handleShow(50)
export default {
  name: '',
  props: {
@@ -2466,7 +2931,6 @@
      isShowExampleFive: false,
      dialogVisible: false,
      thinkingDialog: false,
      stepDialog: false,
      videoPath: "",
      stepIndex: 1,
      thinkIndex: 1,
@@ -2477,103 +2941,32 @@
        txtOne: "",
        txtTwo: "",
      },
      showIndex:0,
      thinkData:[],
      thinkOne: [
        {
          txt: "1:一个函数是不 是偶函数,可以由 函数的图像是否关 于y 轴 对 称 来 判 断;当函数用解析 法表示时,可以用 偶 函 数 的 定 义 来 判断。 偶函数:一般地，设函数f(x)的定义域为D，如果对于任意xED，都有XED，且f(-x)=f(x)，那么函数f(x)就叫作偶函数",
          isShow: true,
        },
        {
          txt: "2:计算f(-x)",
          isShow: false,
        },
        {
          txt: "3:判断f(-x)是否等于f(x)",
          isShow: false,
        },
        "1:一个函数是不 是偶函数,可以由 函数的图像是否关 于y 轴 对 称 来 判 断;当函数用解析 法表示时,可以用 偶 函 数 的 定 义 来 判断。 偶函数:一般地，设函数f(x)的定义域为D，如果对于任意xED，都有XED，且f(-x)=f(x)，那么函数f(x)就叫作偶函数",
        "2:计算f(-x)",
        "3:判断f(-x)是否等于f(x)",
      ],
      stepOne: [
        {
          txt: "1:(1)函数f(x)=3x2+1的定义域是R，对任意XER，都有-XER",
          isShow: true,
        },
        {
          txt: "2:f(-x)=3(-x)2+1=3x2+1=f(x)",
          isShow: false,
        },
      thinkTwo:[
        '因为<i>AB</i>的长度为<i>x</i>（m），<i>BC</i>的长度为（12-<i>x</i>）（m），所以必须满足<i>x</i>＞0且12-<i>x</i>＞0才有实际意义.'
      ],
      dragQuestion: [
        {
          analysisCon: null,
          answer: ['A', 'B', 'C'],
          difficulty: 0,
          id: "7BC7B760",
          isCollect: false,
          isComplete: false,
          isRight: null,
          isUnfold: "",
          isUserAnswer: false,
          number: 1,
          option: [
            {
              img: "",
              index: "010311",
              txt: "胆小的",
              value: "A",
              isShow: true
            },
            {
              img: "",
              index: "010312",
              txt: "善良的",
              value: "B",
              isShow: true
            },
            {
              img: "",
              index: "010313",
              txt: "沉稳的",
              value: "C",
              isShow: true
            },
      thinkThree:[
        '计算该军舰从出发地驶入海港所需要的时间，就可得到函数<i>s</i>=<i>f</i>（<i>t</i>）的定义域.用解析法表示函数后，再画出函数的图像.'
          ],
          optionStyle: "Txt",
          questionType: "drag",
          score: 2,
          stem: {
            0: "蚂蚁队长走路昂首挺胸、步伐坚定，它是一只(",
            1: {
              data: "span",
              num: 0
            },
            2: ")蚂蚁;小蚂蚁走起路来小心翼翼，眼神飘忽不定，它是一只(",
            3: {
              data: "span",
              num: 1
            },
            4: ")蚂蚁;蚂蚁小妹面带微笑，时刻愿意帮助大家，它是一只(",
            5: {
              data: "span",
              num: 2,
            },
            6: " )蚂蚁"
          },
          stemStyle: "RichTxt",
          type: "拖拽题",
          userAnswer: [
            {
              vlaue: '',
              txt: ''
            },
            {
              vlaue: '',
              txt: ''
            },
            {
              vlaue: '',
              txt: ''
            },
          ]
        },
      thinkFour:[
        '首先需明确这个函数的定义域.由于居民用电量不同，其收费标准也不同，所以这是分段函数.其次要厘清自变量<i>x</i>在不同的取值范围内与因变量<i>y</i>之间的对应关系，并列出相应的解析式来解决相关问题.'
      ],
      thinkFive:[
        '首先求出小李从A城到B城和从B城返回A城共花费的时间，明确函数的定义域.小李去B城和返回A城的过程中，<i>y</i>与<i>x</i>分别对应的解析式不相同，所以该函数需用分段函数表示.'
      ],
      thinkSix:[
        '首先需要计算备用材料可修建饲养室新墙的总长；因每间饲养室的周长是定值，所以设<i>AB</i>的长为<i>x</i>（m），就可以用含<i>x</i>的代数式表示<i>BC</i>的长；',
        '再用解析法表示总面积<i>y</i>（m<sup>2</sup>）与<i>x</i>（m）的函数关系；然后利用函数的性质来解决问题.'
      ],
      thinkSeven:[
        '先由图像求出一次函数的解析式，',
        '再根据每月所获利润=（销售单价-进价）×每月销售量，列出每月所获利润<i>w</i>与销售单价<i>x</i>的函数关系.'
      ]
    };
  },
@@ -2609,22 +3002,15 @@
        openMathDiaolog() {
      this.dialogVisible = true;
    },
    openThinkingDialog() {
      this.thinkingDialog = true;
    openDialog(queryData) {
      this.thinkData = queryData
      this.thinkingDialog = !this.thinkingDialog
    },
    showNext(num) {
      const number = this.thinkOne.findIndex((item, index) => index == num);
      this.thinkOne[number].isShow = true;
      if (this.thinkIndex <= 2) {
        this.thinkIndex++;
      }
    closeDialog() {
      this.showIndex = 0
    },
    showNextChange(num) {
      const number = this.stepOne.findIndex((item, index) => index == num);
      this.stepOne[number].isShow = true;
      if (this.stepIndex < 2) {
        this.stepIndex++;
      }
    changeNext() {
      if (this.showIndex < this.thinkData.length - 1) this.showIndex = this.showIndex + 1
    },
    //资源收藏事件
    handleCollectResource(id, md5, resourcePath, resourceType, source, resourceName) {
@@ -2650,9 +3036,6 @@
</script>

<style lang="less" scoped>
  


li {
  list-style: none;
}

 src/books/mathBook/view/components/chapter004.vue

@@ -335,8 +335,8 @@
          <p>
            <span class="zt-ls"><b>例1</b></span>　计算.
          </p>
          <p>
            （1）
          <p class="p-btn" >
            <span>（1）
            <math display="0">
              <mroot>
                <msup>
@@ -347,7 +347,19 @@
                </msup>
                <mn>3</mn>
              </mroot>
            </math>；（2）
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer0 = !isShowAnswer0">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
                （2）
            <math display="0">
              <mroot>
                <msup>
@@ -363,7 +375,19 @@
                </msup>
                <mn>3</mn>
              </mroot>
            </math>；（3）
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer1 = !isShowAnswer1">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （3）
            <math display="0">
              <mroot>
                <msup>
@@ -375,8 +399,17 @@
                <mn>4</mn>
              </mroot>
            </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer2 = !isShowAnswer2">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
          <p class="p-btn" >
            <span>
            （4）
            <math display="0">
              <mroot>
@@ -393,9 +426,27 @@
                </msup>
                <mn>4</mn>
              </mroot>
            </math>；（5） 81的4次方根.
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer3 = !isShowAnswer3">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
          <p class="p-btn" >
            <span>（5） 81的4次方根.</span>
            <span class="btn-box" @click="isShowAnswer4 = !isShowAnswer4">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p v-if="isShowAnswer0" >
            <span class="zt-ls"><b>解</b></span>（1）<math display="0">
              <mroot>
                <msup>
@@ -410,7 +461,7 @@
              <mn>5</mn>
            </math>；
          </p>
          <p>
          <p v-if="isShowAnswer1" >
            （2）
            <math display="0">
              <mroot>
@@ -432,7 +483,7 @@
              <mn>5</mn>
            </math>；
          </p>
          <p>
          <p v-if="isShowAnswer2" >
            （3）
            <math display="0">
              <mroot>
@@ -452,7 +503,7 @@
              <mn>7</mn>
            </math>；
          </p>
          <p>
          <p v-if="isShowAnswer3" >
            （4）
            <math display="0">
              <mroot>
@@ -480,7 +531,7 @@
              <mn>7</mn>
            </math>；
          </p>
          <p>
          <p v-if="isShowAnswer4" >
            （5） 因为（±3）<sup>4</sup>=81，所以81的4次方根是±3，即<math display="0">
              <mo>±</mo>
              <mroot>
@@ -495,7 +546,8 @@
          <p>
            <span class="zt-ls"><b>例2</b></span>　化简.
          </p>
          <p>
          <p class="p-btn" >
            <span>  
            （1）
            <math display="0">
              <mroot>
@@ -513,7 +565,19 @@
                </msup>
                <mn>3</mn>
              </mroot>
            </math>；（2）
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer5 = !isShowAnswer5">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2）
            <math display="0">
              <mroot>
                <msup>
@@ -533,8 +597,16 @@
                <mn>4</mn>
              </mroot>
            </math>.
            </span>
            <span class="btn-box" @click="isShowAnswer6 = !isShowAnswer6">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
          <p v-if="isShowAnswer5" >
            <span class="zt-ls"><b>解</b></span>（1）
            <math display="0">
              <mroot>
@@ -558,7 +630,7 @@
              <mi>a</mi>
            </math>；
          </p>
          <p>
          <p v-if="isShowAnswer6" >
            （2）
            <math display="0">
              <mroot>
@@ -885,7 +957,8 @@
          <p>
            <span class="zt-ls"><b>例3</b></span>　将下列根式用分数指数幂表示（式中字母均为正实数）.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            （1）
            <math display="0">
              <mroot>
@@ -897,7 +970,19 @@
                </msup>
                <mn>4</mn>
              </mroot>
            </math>；（2）
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer7 = !isShowAnswer7">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2）
            <math display="0">
              <mroot>
                <msup>
@@ -908,7 +993,19 @@
                </msup>
                <mn>6</mn>
              </mroot>
            </math>；（3）
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer8 = !isShowAnswer8">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （3）
            <math display="0">
              <mfrac>
                <mn>1</mn>
@@ -923,8 +1020,16 @@
                </mroot>
              </mfrac>
            </math>.
            </span>
            <span class="btn-box" @click="isShowAnswer9 = !isShowAnswer9">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
          <p v-if="isShowAnswer7" >
            <span class="zt-ls"><b>解</b></span>（1）
            <math display="0">
              <mroot>
@@ -948,7 +1053,7 @@
              </msup>
            </math>；
          </p>
          <p>
          <p v-if="isShowAnswer8" >
            （2）
            <math display="0">
              <mroot>
@@ -982,7 +1087,7 @@
              </msup>
            </math>）
          </p>
          <p>
          <p v-if="isShowAnswer9" >
            （3）
            <math display="0">
              <mfrac>
@@ -1026,7 +1131,8 @@
          <p>
            <span class="zt-ls"><b>例4</b></span>　化简（式中字母均为正实数）.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            （1）<math display="0">
              <msup>
                <mn>27</mn>
@@ -1038,7 +1144,19 @@
                  </mfrac>
                </mrow>
              </msup>
            </math>；（2）
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer10 = !isShowAnswer10">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2）
            <math display="0">
              <msup>
                <mrow data-mjx-texclass="INNER">
@@ -1069,8 +1187,16 @@
                </mrow>
              </msup>
            </math>.
            </span>
            <span class="btn-box" @click="isShowAnswer11 = !isShowAnswer11">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
          <p v-if="isShowAnswer10" >
            <span class="zt-ls"><b>解</b></span>（1）<math display="0">
              <msup>
                <mn>27</mn>
@@ -1110,7 +1236,7 @@
              </mfrac>
            </math>；
          </p>
          <p>
          <p v-if="isShowAnswer11" >
            （2）<math display="0">
              <msup>
                <mrow data-mjx-texclass="INNER">
@@ -1337,7 +1463,7 @@
            <p>第四单元 指数函数与对数函数</p>
          </li>
          <li>
            <p><span>119</span></p>
            <p><span>119-120</span></p>
          </li>
        </ul>
        <div class="padding-116">
@@ -1355,7 +1481,8 @@
          <p>
            <span class="zt-ls"><b>例1</b></span>　计算（式中字母均为正实数）.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            （1）<math display="0">
              <msup>
                <mn>16</mn>
@@ -1399,7 +1526,19 @@
                  <mn>0</mn>
                </mrow>
              </msup>
            </math>；（2）
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer12 = !isShowAnswer12">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2）
            <math display="0">
              <msup>
                <mrow data-mjx-texclass="INNER">
@@ -1474,7 +1613,16 @@
                </mrow>
              </msup>
            </math>.
            </span>
            <span class="btn-box" @click="isShowAnswer13 = !isShowAnswer13">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer12" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -1633,6 +1781,15 @@
                    <mo>;</mo>
                  </mtd>
                </mtr>
                </mtable>
              </math>
            </p>
          </div>
          <p  v-if="isShowAnswer13" class="left1">
            <math display="">
              <mtable columnalign="left" columnspacing="1em" rowspacing="4pt">


                <mtr>
                  <mtd>
                    <mtext>（2）</mtext>
@@ -1838,10 +1995,20 @@
              </mtable>
            </math>
          </p>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例2</b></span>　化简（式中字母均为正实数）.
            </span>
            <span class="btn-box" @click="openDialog(thinkOne)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p>
          <p class="p-btn" >
            <span>
            （1）
            <math display="0">
              <msqrt>
@@ -1857,7 +2024,19 @@
                <mn>64</mn>
                <mn>8</mn>
              </mroot>
            </math>；（2）
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer14 = !isShowAnswer14">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2）
            <math display="0">
              <msqrt>
                <msup>
@@ -1907,10 +2086,16 @@
                <mn>6</mn>
              </mroot>
            </math>.
            </span>
            <span class="btn-box" @click="isShowAnswer15 = !isShowAnswer15">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="block">
            <span class="zt-ls2"><b>分析</b></span>　运算思路是将根式转化为分数指数幂，然后再化简运算.
          </p>
          <div v-if="isShowAnswer14" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -2054,6 +2239,12 @@
                  <mo>;</mo>
                </mtd>
              </mtr>
              </mtable>
            </math>
          </div>

          <math v-if="isShowAnswer15" display="">
            <mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
              <mtr>
                <mtd>
                  <mtext>（2）</mtext>
@@ -2307,26 +2498,27 @@
              </mtr>
            </mtable>
          </math>
        </div>
      </div>
    </div>
    <!-- 120 -->
    <div class="page-box" page="127">
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        <ul class="page-header-odd fl al-end">
          <li>120</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例3</b></span>　计算
            2<sup>0</sup>+2<sup>1</sup>+2<sup>2</sup>+2<sup>3</sup>+…+2<i><sup>x</sup></i>（<i>x</i>∈<b>N</b>）.
            </span>
            <span class="btn-box" @click="isShowAnswer16 = !isShowAnswer16">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
            <span class="btn-box" @click="openDialog(thinkTwo)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="block">
            <span
              class="zt-ls2"><b>分析</b></span>　观察这个式子的特点，每一项都是前面一项的2倍（除第1项外）；运算思路可考虑将代数式每项乘2后再与原式相减.数学上把这种运算方法叫作“错位相减”.
          </p>
          <div v-if="isShowAnswer16" >
          <p>
            <span class="zt-ls"><b>解</b></span> 令
          </p>
@@ -2436,6 +2628,7 @@
          <p>
            所以，　2<sup>0</sup>+2<sup>1</sup>+2<sup>2</sup>+2<sup>3</sup>+…+2<i><sup>x</sup></i>=2<i><sup>x+1</sup></i>-1.
          </p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -2445,6 +2638,9 @@
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@@ -2641,8 +2837,20 @@
          <p>
            <b>例</b> 已知指数函数<i>f</i>（<i>x</i>）=<i>a<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1），且<i>f</i>（3）=125.
          </p>
          <p>（1） 求函数<i>f</i>（<i>x</i>）的解析式；</p>
          <p>
          <p class="p-btn" >
            <span>
              （1） 求函数<i>f</i>（<i>x</i>）的解析式；
            </span>
            <span class="btn-box" @click="isShowAnswer17 = !isShowAnswer17">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
            （2） 求<i>f</i>（0），<i>f</i>（2），<i>f</i>（-2），<math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
@@ -2654,12 +2862,20 @@
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>的值.
            </span>
            <span class="btn-box" @click="isShowAnswer18 = !isShowAnswer18">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
          <p v-if="isShowAnswer17" >
            <span class="zt-ls"><b>解</b></span>（1）
            因为<i>f</i>（<i>x</i>）=<i>a<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1），且<i>f</i>（3）=125，所以<i>a</i><sup>3</sup>=125，解得<i>a</i>=5，于是<i>f</i>（<i>x</i>）=5<i><sup>x</sup></i>.
          </p>
          <p>
          <p v-if="isShowAnswer18">
            （2）
            <i>f</i>（0）=5<sup>0</sup>=1，<i>f</i>（2）=5<sup>2</sup>=25，<math display="0">
              <mi>f</mi>
@@ -2952,8 +3168,17 @@
          <p class="center">
            <img class="img-a" alt="" src="../../assets/images/0136-1.jpg" />
          </p>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例1</b></span>　判断下列函数哪些是指数函数，并画出函数图像验证.
            </span>
            <span class="btn-box" @click="isShowAnswer19 = !isShowAnswer19">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （1） <i>y</i>=0.5<i><sup>x</sup></i>；（2） <i>y</i>=2×3<i><sup>x</sup></i>；（3） <i>y</i>=<i>x</i><sup>2</sup>.
@@ -2971,6 +3196,7 @@
              在形式上与指数函数相似，但不符合指数函数的定义，我们从其函数图像可以看到没有过定点（0，1）.
            </p>
          </div>
          <div v-if="isShowAnswer19" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
            依据指数函数<i>y</i>=<i>a<sup>x</sup></i>的定义，<i>y</i>=0.5<i><sup>x</sup></i>是指数函数，<i>y</i>=2×3<i><sup>x</sup></i>和<i>y</i>=<i>x</i><sup>2</sup>不是指数函数.画出函数图像（如图4-4所示），函数<i>y</i>=0.5<i><sup>x</sup></i>的图像符合指数函数图像的特征；函数<i>y</i>=2×3<i><sup>x</sup></i>的图像虽与指数函数图像很相似，但并没有过定点（0，1）；函数<i>y</i>=<i>x</i><sup>2</sup>的图像是二次函数的图像.
@@ -2979,6 +3205,8 @@
            <img class="img-b" alt="" src="../../assets/images/0136-2.jpg" />
          </p>
          <p class="img">图4-4</p>
          </div>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
@@ -2995,7 +3223,7 @@
    <div class="page-box" page="133">
      <div v-if="showPageList.indexOf(133) > -1">
        <ul class="page-header-odd fl al-end">
          <li>126</li>
          <li>126-127</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
@@ -3003,8 +3231,29 @@
          <p>
            <span class="zt-ls"><b>例2</b></span>　判断下列函数在（-∞，+∞）内的单调性.
          </p>
          <p>
            （1） <i>y</i>=4<i><sup>x</sup></i>；（2） <i>y</i>=3<i><sup>-x</sup></i>；（3）
          <p class="p-btn" >
            <span>（1） <i>y</i>=4<i><sup>x</sup></i>；</span>
            <span class="btn-box" @click="isShowAnswer20 = !isShowAnswer20">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（2） <i>y</i>=3<i><sup>-x</sup></i>；</span>
            <span class="btn-box" @click="isShowAnswer21 = !isShowAnswer21">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （3）
            <math display="0">
              <mi>y</mi>
              <mo>=</mo>
@@ -3018,10 +3267,25 @@
                </mrow>
              </msup>
            </math>.
            </span>
            <span class="btn-box" @click="isShowAnswer22 = !isShowAnswer22">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer20" >
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 因为4＞1 ， 所以<i>y</i>=4<i><sup>x</sup></i>在（-∞，+∞）内是增函数（如图4-5所示）.
          </p>
            <p class="center">
                <img class="img-f" alt="" src="../../assets/images/0137-7.jpg" />
              </p>
              <p class="img">图4-5</p>
          </div>
          <div v-if="isShowAnswer21" > 
          <p>
            （2）
            <math display="0">
@@ -3076,6 +3340,12 @@
              <mn>1</mn>
            </math>，所以<i>y</i>=3<i><sup>-x</sup></i>在（-∞，+∞）内是减函数（如图4-6所示）.
          </p>
            <p class="center">
                <img class="img-f" alt="" src="../../assets/images/0137-8.jpg" />
              </p>
              <p class="img">图4-6</p>
          </div>
          <div v-if="isShowAnswer22" > 
          <p>
            （3）<math display="0">
              <mi>y</mi>
@@ -3141,46 +3411,62 @@
              </msup>
            </math>在（-∞，+∞）内是增函数（如图4-7所示）.
          </p>
          <ul class="fl">
            <li>
              <p class="center">
                <img class="img-a" alt="" src="../../assets/images/0137-7.jpg" />
              </p>
              <p class="img">图4-5</p>
            </li>
            <li>
              <p class="center">
                <img class="img-a" alt="" src="../../assets/images/0137-8.jpg" />
              </p>
              <p class="img">图4-6</p>
            </li>
            <li>
              <p class="center">
                <img class="img-a" alt="" src="../../assets/images/0137-9.jpg" />
                <img class="img-f" alt="" src="../../assets/images/0137-9.jpg" />
              </p>
              <p class="img">图4-7</p>
            </li>
          </ul>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例3</b></span>　比较下列各题中两个值的大小.
            </span>
            <span class="btn-box" @click="openDialog(thinkThree)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p>
            （1） 1.8<sup>2.5</sup>与1.8<sup>3</sup>；（2）
          <p class="p-btn" >
            <span>
              （1） 1.8<sup>2.5</sup>与1.8<sup>3</sup>；
            </span>
            <span class="btn-box" @click="isShowAnswer23 = !isShowAnswer23">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2）
            0.9<sup>-0.2</sup>与0.9<sup>-0.3</sup>.
            </span>
            <span class="btn-box" @click="isShowAnswer24 = !isShowAnswer24">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="block">
            <span
              class="zt-ls2"><b>分析</b></span>　1.8<sup>2.5</sup>和1.8<sup>3</sup>分别可以看作<i>y</i>=1.8<i><sup>x</sup></i>在<i>x</i>=2.5和<i>x</i>=3处的函数值，这样就可以利用函数的单调性来比较函数值的大小.0.9<sup>-0.2</sup>和0.9<sup>-0.3</sup>分别可以看作<i>y</i>=0.9<i><sup>x</sup></i>在<i>x</i>=-0.2和<i>x</i>=-0.3处的函数值，同样可以利用函数的单调性来比较函数值的大小.
          </p>
          <div v-if="isShowAnswer23" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 因为<i>y</i>=1.8<i><sup>x</sup></i>是<b>R</b>上的增函数，且2.5＜3，所以
          </p>
          <p class="center">1.8<sup>2.5</sup>＜1.8<sup>3</sup>.</p>
          </div>
          <div v-if="isShowAnswer24" > 
          <p>
            （2） 因为<i>y</i>=0.9<i><sup>x</sup></i>是<b>R</b>上的减函数，且-0.2＞-0.3，所以
          </p>
          <p class="center">0.9<sup>-0.2</sup>＜0.9<sup>-0.3</sup>.</p>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例4</b></span>　求函数<math display="0">
              <mi>y</mi>
              <mo>=</mo>
@@ -3195,36 +3481,52 @@
                <mn>4</mn>
              </msqrt>
            </math>的定义域.
            </span>
            <span class="btn-box" @click="isShowAnswer25 = !isShowAnswer25">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer25" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
            要使函数有意义，必须满足2<i><sup>x</sup></i>-4≥0，即2<i><sup>x</sup></i>≥4，又因为<i>y</i>=2<i><sup>x</sup></i>是增函数，所以<i>x</i>≥2.
          </p>
          <p>故函数的定义域为2，+∞）.</p>
        </div>
      </div>
    </div>
    <!-- 127 -->
    <div class="page-box" page="134">
      <div v-if="showPageList.indexOf(134) > -1">
        <ul class="page-header-box">
          <li>
            <p>第四单元 指数函数与对数函数</p>
          </li>
          <li>
            <p><span>127</span></p>
          </li>
        </ul>

        <div class="padding-116">
          <p>
            <span
              class="zt-ls"><b>例5</b></span>　已知指数函数<i>f</i>（<i>x</i>）=<i>a<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1）的图像过点（3，27）.
          </p>
          <p>
            （1） 求<i>f</i>（-1） 的值；（2）
            若<i>f</i>（m）≥9，求<i>m</i>的取值范围.
          <p class="p-btn" >
            <span>
              （1） 求<i>f</i>（-1） 的值；
            </span>
            <span class="btn-box" @click="isShowAnswer26 = !isShowAnswer26">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2）
              若<i>f</i>（m）≥9，求<i>m</i>的取值范围.
            </span>
            <span class="btn-box" @click="isShowAnswer27 = !isShowAnswer27">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer26" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 图像过点（3，27），即<i>x</i>=3时，<i>f</i>（3）=27.
          </p>
@@ -3255,6 +3557,8 @@
              </mfrac>
            </math>.
          </p>
          </div>
          <div v-if="isShowAnswer27" > 
          <p>
            （2）
            因为<i>f</i>（<i>m</i>）=3<i><sup>m</sup></i>，所以得到3<i><sup>m</sup></i>≥9，即3<i><sup>m</sup></i>≥3<sup>2</sup>.
@@ -3263,6 +3567,7 @@
            函数<i>y</i>=3<i><sup>x</sup></i>在定义域内是增函数.
          </p>
          <p>因此，<i>m</i>≥2，即<i>m</i>的取值范围为[2，+∞）.</p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -3272,6 +3577,9 @@
          </div>
        </div>
      </div>
    </div>
    <!-- 127 -->
    <div class="page-box hidePage" page="134">
    </div>
    <!-- 128 -->
    <div class="page-box" page="135">
@@ -3386,8 +3694,17 @@
            <examinations :cardList="questionData[137]" :hideCollect="true" sourceType="json" v-if="questionData">
            </examinations>
          </div>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例1</b></span>　把下列指数式写成对数式.
            </span> 
            <span class="btn-box" @click="isShowAnswer28 = !isShowAnswer28">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （1） 5<sup>4</sup>=625；（2）
@@ -3405,7 +3722,7 @@
              <mn>16</mn>
            </math>；（3） 10<sup>-2</sup>=0.01.
          </p>
          <p>
          <p v-if="isShowAnswer28" >
            <span class="zt-ls"><b>解</b></span>（1） log<sub>5</sub>625=4；（2）
            <math display="0">
              <msub>
@@ -3422,8 +3739,17 @@
              </mfrac>
            </math>；（3） lg0.01=-2.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例2</b></span>　把下列对数式写成指数式.
            </span>
            <span class="btn-box" @click="isShowAnswer29 = !isShowAnswer29">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （1） log<sub>3</sub>243=5；（2）
@@ -3445,7 +3771,7 @@
              <mn>3</mn>
            </math>；（3） <i>ln</i>1=0.
          </p>
          <p>
          <p v-if="isShowAnswer29" >
            <span class="zt-ls"><b>解</b></span>（1） 3<sup>5</sup>=243；（2）
            <math display="0">
              <msup>
@@ -3468,8 +3794,17 @@
              </mfrac>
            </math>；（3） <i>e</i><sup>0</sup>=1.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例3</b></span>　求下列各式中<i>N</i>的值.
            </span>
            <span class="btn-box" @click="isShowAnswer30 = !isShowAnswer30">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （1） lg<i>N</i>=-3；（2）
@@ -3488,6 +3823,7 @@
              </mfrac>
            </math>.
          </p>
          <div v-if="isShowAnswer30" >
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 由lg<i>N</i>=-3，得<i>N</i>=10<sup>-3</sup>=0.001；
          </p>
@@ -3547,13 +3883,24 @@
              <mn>4</mn>
            </math>.
          </p>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例4</b></span>　求下列各式中<i>x</i>的值.
            </span>
            <span class="btn-box" @click="isShowAnswer31 = !isShowAnswer31">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （1） log <sub>2</sub>8=<i>x</i>；（2） log
            <sub>4</sub>4<sup>5</sup>=<i>x</i>.
          </p>
          <div v-if="isShowAnswer31" >
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 由log
            <sub>2</sub>8=<i>x</i>，得2<i><sup>x</sup></i>=8，即2<i><sup>x</sup></i>=2<sup>3</sup>，所以<i>x</i>=3；
@@ -3561,16 +3908,36 @@
          <p>
            （2） 由log <sub>4</sub>4<sup>5</sup>=<i>x</i>，得4<i><sup>x</sup></i>=4<sup>5</sup>，所以<i>x</i>=5.
          </p>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例5</b></span>　求下列各式的值.
            </span>
            <span class="btn-box" @click="isShowAnswer32 = !isShowAnswer32">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
            <span class="btn-box" @click="openDialog(thinkFour)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
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                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p>
            （1） log<sub>5</sub>1；（2） log<sub>7</sub>7；（3） lg 10；（4）
            ln e.
          </p>
          <div v-if="isShowAnswer32" >
          <p>
            <span class="zt-ls2"><b>分析</b></span>　利用性质“1的对数为0”和“底数的对数为1” 直接得答案，不必转化成指
              <span class="zt-ls"><b>解</b></span>（1） log<sub>5</sub>1=0；（2） log<sub>7</sub>7=1；
          </p>
            <p>（3） lg10=log<sub>10</sub>10=1；（4） ln e=log<sub>e</sub>e=1.</p>
          </div>
        </div>
      </div>
    </div>
@@ -3586,11 +3953,6 @@
          </li>
        </ul>
        <div class="padding-116">
          <p>数式.</p>
          <p>
            <span class="zt-ls"><b>解</b></span>（1） log<sub>5</sub>1=0；（2） log<sub>7</sub>7=1；
          </p>
          <p>（3） lg10=log<sub>10</sub>10=1；（4） ln e=log<sub>e</sub>e=1.</p>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -3713,12 +4075,34 @@
            <examinations :cardList="questionData[139]" :hideCollect="true" sourceType="json" v-if="questionData">
            </examinations>
          </div>
          <p>
          <p class="p-btn" >
            <span>
            <span
              class="zt-ls"><b>例1</b></span>　用log<i><sub>a</sub>x</i>，log<i><sub>a</sub>y</i>，log<i><sub>a</sub>z</i>表示下列各式（式中字母均为正实数且<i>a</i>≠1）.
            </span>
            <span class="btn-box" @click="openDialog(thinkFive)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
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                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p>
            （1） log<i><sub>a</sub></i>（<i>x</i><sup>2</sup><i>yz</i><sup>3</sup>）；（2）<math display="0">
          <p class="p-btn" >
            <span>
              （1） log<i><sub>a</sub></i>（<i>x</i><sup>2</sup><i>yz</i><sup>3</sup>）；
            </span>
            <span class="btn-box" @click="isShowAnswer33 = !isShowAnswer33">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2）<math display="0">
              <msub>
                <mi>log</mi>
                <mrow>
@@ -3738,7 +4122,19 @@
                  <mi>z</mi>
                </mrow>
              </mfrac>
            </math>；（3）
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer34 = !isShowAnswer34">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （3）
            <math display="0">
              <msub>
                <mi>log</mi>
@@ -3762,10 +4158,16 @@
                </mrow>
              </mfrac>
            </math>.
            </span>
            <span class="btn-box" @click="isShowAnswer35 = !isShowAnswer35">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="block">
            <span class="zt-ls2"><b>分析</b></span>　利用对数运算性质进行化简运算.
          </p>
          <div v-if="isShowAnswer33" >            
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -3865,7 +4267,8 @@
              <mo>;</mo>
            </math>
          </p>
          <p class="left1">
          </div>
          <p class="left1"  v-if="isShowAnswer34">
            <math display="">
              <mo stretchy="false">（2）</mo>
              <msub>
@@ -3976,7 +4379,7 @@
              <mo>;</mo>
            </math>
          </p>
          <p class="left1">
          <p class="left1" v-if="isShowAnswer35" >
            <math display="">
              <mo stretchy="false">（3）</mo>
              <msub>
@@ -4068,7 +4471,8 @@
          <p>
            <span class="zt-ls"><b>例2</b></span>　计算.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            （1）
            <math display="0">
              <msub>
@@ -4081,25 +4485,42 @@
                <mn>25</mn>
                <mn>3</mn>
              </mroot>
            </math>；（2） log <sub>3</sub>（9<sup>3</sup>×3<sup>5</sup>）；（3） log
            <sub>7</sub>56-log<sub>7</sub>8.
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer36 = !isShowAnswer36">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
        </div>
      </div>
    </div>
    <!-- 133 -->
    <div class="page-box" page="140">
      <div v-if="showPageList.indexOf(140) > -1">
        <ul class="page-header-box">
          <li>
            <p>第四单元 指数函数与对数函数</p>
          </li>
          <li>
            <p><span>133</span></p>
          </li>
        </ul>

        <div class="padding-116">
          <p class="p-btn" >
            <span>
              （2） log <sub>3</sub>（9<sup>3</sup>×3<sup>5</sup>）；
            </span>
            <span class="btn-box" @click="isShowAnswer37 = !isShowAnswer37">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （3） log
              <sub>7</sub>56-log<sub>7</sub>8.
            </span>
            <span class="btn-box" @click="isShowAnswer38 = !isShowAnswer38">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer36" >
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -4172,7 +4593,8 @@
              <mo>;</mo>
            </math>
          </p>
          <p class="left1">
          </div>
          <p v-if="isShowAnswer37" class="left1">
            <math display="">
              <mo stretchy="false">（2）</mo>
              <msub>
@@ -4264,7 +4686,7 @@
              <mo>;</mo>
            </math>
          </p>
          <p class="left1">
          <p v-if="isShowAnswer38" class="left1">
            <math display="">
              <mo stretchy="false">（3）</mo>
              <msub>
@@ -4310,6 +4732,25 @@
              <mo>.</mo>
            </math>
          </p>
        </div>
      </div>
    </div>
    <!-- 133 -->
    <div class="page-box" page="140">
      <div v-if="showPageList.indexOf(140) > -1">
        <ul class="page-header-box">
          <li>
            <p>第四单元 指数函数与对数函数</p>
          </li>
          <li>
            <p><span>133</span></p>
          </li>
        </ul>

        <div class="padding-116">



          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -4526,9 +4967,19 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例1</b></span>　求log<sub>27</sub>8·log <sub>32</sub>9的值.
            </span>
            <span class="btn-box" @click="isShowAnswer39 = !isShowAnswer39">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer39" >
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -4675,10 +5126,21 @@
              </mtr>
            </mtable>
          </math>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span
              class="zt-ls"><b>例2</b></span>　求证：log<i><sub>a</sub>b</i>·log<i><sub>b</sub>c</i>·log<i><sub>c</sub>a</i>=1（<i>a</i>，<i>b</i>，<i>c</i>均为正实数，且均不等于1）.
            </span>
            <span class="btn-box" @click="isShowAnswer40 = !isShowAnswer40">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer40" >
          <p>
            <b>证明</b>
            <math display="0">
@@ -4816,8 +5278,18 @@
            <mtext>.&nbsp;</mtext>
          </math>
          <p>这个式子叫<b>对数恒等式</b>.</p>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例3</b></span>　求下列各式的值.
            </span>
            <span class="btn-box" @click="isShowAnswer41 = !isShowAnswer41">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （1）
@@ -4866,6 +5338,7 @@
              </msup>
            </math>.
          </p>
          <div v-if="isShowAnswer41" >
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -5030,6 +5503,7 @@
              <mo>.</mo>
            </math>
          </p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -5139,7 +5613,8 @@
              真数的取值范围为（0，+∞），所以对数函数自变量<i>x</i>的取值范围为（0，+∞）.
            </p>
          </div>
          <p>
          <p class="p-btn" >
            <span>
            <span
              class="zt-ls"><b>例1</b></span>　已知对数函数<i>f</i>（<i>x</i>）=log<i><sub>a</sub>x</i>（<i>a</i>＞0，且<i>a</i>≠1），且<i>f</i>（9）=
            2，求<i>f</i>（3），<i>f</i>（1），<math display="0">
@@ -5153,10 +5628,23 @@
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>的值.
            </span>
            <span class="btn-box" @click="isShowAnswer42 = !isShowAnswer42">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
            <span class="btn-box" @click="openDialog(thinkSix)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="block">
            <span class="zt-ls2"><b>分析</b></span>　首先根据条件确定底数<i>a</i>，然后再计算对应函数值.
          </p>
          <div v-if="isShowAnswer42" >
          <p>
            <span class="zt-ls"><b>解</b></span> 因为<i>f</i>（9）=2，得2=log<i><sub>a</sub></i>9.
          </p>
@@ -5209,19 +5697,44 @@
              <mn>3</mn>
            </math>.
          </p>
          </div>
          <p>
            <span class="zt-ls"><b>例2</b></span>　求下列函数的定义域.
          </p>
          <p>
            （1） <i>y</i>=log <sub>0.5</sub>（<i>x</i>-3）；（2）
            <i>y</i>=log<sub>3</sub>（4-<i>x</i><sup>2</sup>）.
          <p class="p-btn" >
            <span>
              （1） <i>y</i>=log <sub>0.5</sub>（<i>x</i>-3）；
            </span>
            <span class="btn-box" @click="isShowAnswer43 = !isShowAnswer43">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2）
              <i>y</i>=log<sub>3</sub>（4-<i>x</i><sup>2</sup>）.
            </span>
            <span class="btn-box" @click="isShowAnswer44 = !isShowAnswer44">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer43" >
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 要使函数有意义，必须满足<i>x</i>-3＞0，解得<i>x</i>＞3.
          </p>
          <p>
            所以，<i>y</i>=log <sub>0.5</sub>（<i>x</i>-3）的定义域是（3，+∞）.
          </p>
          </div>
          <div v-if="isShowAnswer44" > 
          <p>
            （2） 要使函数有意义，必须满足4-<i>x</i><sup>2</sup>＞0，解得
            -2＜<i>x</i>＜2.
@@ -5229,6 +5742,7 @@
          <p>
            所以，<i>y</i>=log<sub>3</sub>（4-<i>x</i><sup>2</sup>）的定义域是（-2，2）.
          </p>
          </div>
        </div>
      </div>
    </div>
@@ -5425,29 +5939,97 @@
            <examinations :cardList="questionData[146]" :hideCollect="true" sourceType="json"
            v-if="questionData" ></examinations>
          </div>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例1</b></span>　比较下列各组数中两个值的大小.
            </span>
            <span class="btn-box" @click="openDialog(thinkSeven)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p>
            （1） log<sub>2</sub>5.3 与log<sub>2</sub>4.7；（2） log
          <p class="p-btn" >
            <span>
              （1） log<sub>2</sub>5.3 与log<sub>2</sub>4.7；
            </span>
            <span class="btn-box" @click="isShowAnswer45 = !isShowAnswer45">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2） log
            <sub>0.2</sub>7与log <sub>0.2</sub>9；
            </span>
            <span class="btn-box" @click="isShowAnswer46 = !isShowAnswer46">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （3） log<sub>5</sub>4与1；（4）log<sub>3</sub>4与log
          <p class="p-btn" >
            <span>
              （3） log<sub>5</sub>4与1；
            </span>
            <span class="btn-box" @click="isShowAnswer47 = !isShowAnswer47">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （4）log<sub>3</sub>4与log
            <sub>0.3</sub>4.
            </span>
            <span class="btn-box" @click="isShowAnswer48 = !isShowAnswer48">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="block">
            <span class="zt-ls2"><b>分析</b></span>　若两个对数的底数相同，可利用对数函数的单调性直接比较；若底数不同，可采用先与中间量（通常是0或1）进行比较，再利用不等式传递性得出结论.
          </p>
          <div v-if="isShowAnswer45" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1）
            因为底数2＞1，所以<i>y</i>=log<sub>2</sub><i>x</i>在区间（0，+∞）上是增函数，函数图像如图4-10所示.
          </p>
          <p>又因为5.3＞4.7，所以log<sub>2</sub>5.3＞log<sub>2</sub>4.7.</p>
            <p class="center">
                <img class="img-f" alt="" src="../../assets/images/0151-1.jpg" />
              </p>
              <p class="img">图4-10</p>
          </div>
          <div v-if="isShowAnswer46" > 
          <p>
            （2） 因为底数0＜0.2＜1，所以<i>y</i>=log <sub>0.2</sub><i>x</i>在区间（0，+∞）上是减函数，函数图像如图4-11所示.
          </p>
          <p>又因为7＜9，所以log <sub>0.2</sub>7＞log <sub>0.2</sub>9.</p>
            <p class="center">
                <img class="img-f" alt="" src="../../assets/images/0151-2.jpg" />
              </p>
              <p class="img">图4-11</p>
          </div>
          <p v-if="isShowAnswer47">
            （3） log<sub>5</sub>4＜log<sub>5</sub>5=1，即log<sub>5</sub>4＜1.
          </p>
          <p v-if="isShowAnswer48" >
            （4） 因为 log<sub>3</sub>4＞log<sub>3</sub>1=0，log
            <sub>0.3</sub>4＜log <sub>0.3</sub>1=0，所以 log<sub>3</sub>4＞log
            <sub>0.3</sub>4.
          </p>
        </div>
      </div>
    </div>
@@ -5461,32 +6043,23 @@
        </ul>
        <div class="padding-116">
          <p>
            （3） log<sub>5</sub>4＜log<sub>5</sub>5=1，即log<sub>5</sub>4＜1.
          </p>
          <ul class="fl">
            <li>
              <p class="center">
                <img class="img-a" alt="" src="../../assets/images/0151-1.jpg" />
              </p>
              <p class="img">图4-10</p>
            </li>
            <li>
              <p class="center">
                <img class="img-a" alt="" src="../../assets/images/0151-2.jpg" />
              </p>
              <p class="img">图4-11</p>
            </li>
          </ul>
          <p>
            （4） 因为 log<sub>3</sub>4＞log<sub>3</sub>1=0，log
            <sub>0.3</sub>4＜log <sub>0.3</sub>1=0，所以 log<sub>3</sub>4＞log
            <sub>0.3</sub>4.
          </p>
          <p>
            <span class="zt-ls"><b>例2</b></span>　解下列不等式.
          </p>
          <p>
            （1）log <sub>4</sub><i>x</i>＜log<sub>4</sub>5；（2）
          <p class="p-btn" >
            <span>
              （1）log <sub>4</sub><i>x</i>＜log<sub>4</sub>5；
            </span>
            <span class="btn-box" @click="isShowAnswer49 = !isShowAnswer49">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2）
            <math display="0">
              <msub>
                <mi>log</mi>
@@ -5502,13 +6075,24 @@
              <mo>＞</mo>
              <mn>1</mn>
            </math>.
            </span>
            <span class="btn-box" @click="isShowAnswer50 = !isShowAnswer50">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer49" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 因为<i>y</i>=log
            4<i>x</i>在（0，+∞）上是增函数，所以<i>x</i>＜5.
          </p>
          <p>又因为<i>x</i>＞0，所以0＜<i>x</i>＜5.</p>
          <p>所以不等式的解集为（0，5）.</p>
          </div>
          <div v-if="isShowAnswer50" > 
          <p>
            （2）
            <math display="0">
@@ -5604,6 +6188,7 @@
              </mrow>
            </math>）.
          </p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -5643,8 +6228,28 @@
            178万人，其中城镇常住人口90
            199万人，占总人口的比例（常住人口城镇化率）为63.89%，与2010年相比，提高了14.21个百分点.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            （1） 假设此后每年都增加700万人口，20年后我国大陆人口总数是多少？
            </span>
            <span class="btn-box" @click="isShowAnswer51 = !isShowAnswer51">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
            <span class="btn-box" @click="openDialog(thinkEight)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p v-if="isShowAnswer51" >
            <span class="zt-ls"><b>解</b></span>（1） 因为每年增加700万人口，20年共增加20×700万=14
            000万人口，因此20年后我国大陆人口为155 178万（15.517 8亿）.
          </p>
        </div>
      </div>
@@ -5660,41 +6265,31 @@
            <p>第四单元 指数函数与对数函数</p>
          </li>
          <li>
            <p><span>143</span></p>
            <p><span>143-144</span></p>
          </li>
        </ul>
        <div class="padding-116">
          <p>
          <p class="p-btn" >
            <span>
            （2）
            假设此后每年人口的平均增长率是1%（每年都在前一年基础上增加1%），20年后我国大陆人口总数约为多少？（单位：万，结果精确到0.01）
            </span>
            <span class="btn-box" @click="isShowAnswer52 = !isShowAnswer52">
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            </span>
          </p>
          <p class="block">
            <b>分析</b>（1）
            这是经济社会中的“线性增长”现象，即每年增加量保持不变，每年增加700万人口，20年共增加14
            000万人口，因此总共人口为155 178万.
          </p>
          <p class="block">
            （2）
            这是经济社会中的“指数增长”现象，即每年按照一定的增长率（成倍数）增长.我们首先考查逐年增长的情况，从中发现每一年都是前一年的（1+1%）倍（也可采用后一年与前一年的比值发现规律），即呈指数增长，最后利用指数函数知识解决问题.
          </p>
          <p class="block">2020年年末 人口约为141 178万；</p>
          <p class="block">经过1年 人口约为141 178（1+1%）万；</p>
          <p class="block">
            经过2年 人口约为141 178（1+1%）（1+1%）=141
            178（1+1%）<sup>2</sup>万；
          </p>
          <p class="block">
            经过3年 人口约为141 178（1+1%）<sup>2</sup>（1+1%）=141
            178（1+1%）<sup>3</sup>万；
          </p>
          <p class="block">……</p>
          <p class="block">
            经过<i>x</i>年 人口约为141 178（1+1%）<i><sup>x</sup></i>万.
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 因为每年增加700万人口，20年共增加20×700万=14
            000万人口，因此20年后我国大陆人口为155 178万（15.517 8亿）.
          </p>
          <div v-if="isShowAnswer52" > 
          <p>（2） 设经过<i>x</i>年，我国人口为<i>y</i>万，由题意得</p>
          <p class="center">
            <i>y</i>=141 178（1+1%）<i><sup>x</sup></i>.
@@ -5706,6 +6301,7 @@
            178万；假设每年人口的平均增长率是1%，经过20年后我国大陆人口约为172
            263.99万.
          </p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
          </p>
@@ -5715,18 +6311,6 @@
          <p>
            一般地，形如<i>y</i>=<i>ka<sup>x</sup></i>（<i>a</i>＞0，且<i>a</i>≠1，<i>k</i>≠0）的函数称为<b>指数型函数</b>，这是生活实际中常见的和实用的函数模型.其中，当<i>a</i>＞1时，该函数叫作指数增长模型，如我们常说的“指数爆炸”现象所蕴含的就是这种模型；当0＜<i>a</i>＜1时，该函数叫作指数衰减模型，如考古工作中的碳14衰减现象所蕴含的就是这种模型.
          </p>
        </div>
      </div>
    </div>
    <!-- 144 -->
    <div class="page-box" page="151">
      <div v-if="showPageList.indexOf(151) > -1">
        <ul class="page-header-odd fl al-end">
          <li>144</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p>
            <span class="zt-ls"><b>例2</b></span>　2020年12月8日，中国、尼泊尔两国共同向全世界正式宣布，世界第一高峰珠穆朗玛峰的最新海拔高程为8
            848.86
@@ -5736,13 +6320,32 @@
            来近似描述，其中<i>c</i>，<i>k</i>可看成常量.又知登顶过程中，海平面的大气压强为1.013×10<sup>5</sup>
            Pa，北坳营地海拔7 028 m，大气压强约为4.21×10<sup>4</sup>Pa.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            （1） 当大气压强为3.81×10<sup>4</sup> <i>Pa</i> 时，海拔高程是多少？
            </span>
            <span class="btn-box" @click="isShowAnswer53 = !isShowAnswer53">
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                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
          <p class="p-btn" >
            <span>
            （2） 当测绘人员在登顶过程中测得其所在位置的海拔高程为8 844.43
            m时，大气压强为多少？
            </span>
            <span class="btn-box" @click="isShowAnswer54 = !isShowAnswer54">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
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                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer53" > 
          <p>
            <span class="zt-ls"><b>解</b></span> 海平面的海拔高程为0 m.将
          </p>
@@ -5776,6 +6379,8 @@
            所以，当大气压强为3.81×10<sup>4</sup> <i>Pa</i>时，海拔高程约为7
            827.090 m.
          </p>
          </div>
          <div v-if="isShowAnswer54" > 
          <p>（2） 把<i>y</i>=8 844.43代入①式，</p>
          <p class="center">8 844.43=-8 004.203 ln <i>x</i>+92 255.180，</p>
          <p class="center">
@@ -5794,6 +6399,10 @@
          </p>
        </div>
      </div>
      </div>
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@@ -6204,11 +6813,68 @@
    <div class="page-box hidePage" page="158"></div>
    <!-- 152 -->
    <div class="page-box hidePage" page="159"></div>
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            fill="#1296db" p-id="5068" />
          <path
            d="M2.257993 117.980154 415.470783 531.192944 512 627.722161 608.529217 531.192944 1021.742007 117.980154 925.212789 21.450937 512 434.663727 98.787211 21.450937Z"
            fill="#1296db" p-id="5069" />
        </svg>
      </div>
    </el-dialog>
  </div>
</template>

<script>
import examinations from "@/components/examinations/index.vue";
const handleShow = (num) => {
  const obj = {}
  for (let index = 0; index < num; index++) {
    obj['isShowAnswer' + index] = false
  }
  return obj
}
const showObj = handleShow(60)
export default {
  name: "",
  props: {
@@ -6222,11 +6888,66 @@
  },
  components: { examinations },
  data() {
    return {};
    return {
      ...showObj,
      showIndex:0,
      thinkingDialog: false,
      thinkData:[],
      thinkOne:[
        '运算思路是将根式转化为分数指数幂，然后再化简运算.'
      ]
      ,
      thinkTwo:[
        '观察这个式子的特点，每一项都是前面一项的2倍（除第1项外）；',
        '运算思路可考虑将代数式每项乘2后再与原式相减.数学上把这种运算方法叫作“错位相减”.'
      ],
      thinkThree:[
        '1.8<sup>2.5</sup>和1.8<sup>3</sup>分别可以看作<i>y</i>=1.8<i><sup>x</sup></i>在<i>x</i>=2.5和<i>x</i>=3处的函数值，这样就可以利用函数的单调性来比较函数值的大小.0.9<sup>-0.2</sup>和0.9<sup>-0.3</sup>分别可以看作<i>y</i>=0.9<i><sup>x</sup></i>在<i>x</i>=-0.2和<i>x</i>=-0.3处的函数值，同样可以利用函数的单调性来比较函数值的大小.'
      ],
      thinkFour:[
        '利用性质“1的对数为0”和“底数的对数为1” 直接得答案，不必转化成指数式.'
      ],
      thinkFive:[
        '利用对数运算性质进行化简运算.'
      ],
      thinkSix:[
        '首先根据条件确定底数<i>a</i>，然后再计算对应函数值.'
      ],
      thinkSeven:[
        '若两个对数的底数相同，可利用对数函数的单调性直接比较；若底数不同，可采用先与中间量（通常是0或1）进行比较，再利用不等式传递性得出结论.'
      ],
      thinkEight:[
        '（1）这是经济社会中的“线性增长”现象，即每年增加量保持不变，每年增加700万人口，20年共增加14000万人口，因此总共人口为155 178万.'
      ],
      thinkNine:[
        ' 这是经济社会中的“指数增长”现象，即每年按照一定的增长率（成倍数）增长.我们首先考查逐年增长的情况，从中发现每一年都是前一年的（1+1%）倍（也可采用后一年与前一年的比值发现规律），即呈指数增长，最后利用指数函数知识解决问题.',
        '2020年年末 人口约为141 178万；',
        '经过1年 人口约为141 178（1+1%）万；',
        '经过2年 人口约为141 178（1+1%）（1+1%）=141   178（1+1%）<sup>2</sup>万；',
        '经过3年 人口约为141 178（1+1%）<sup>2</sup>（1+1%）=141   178（1+1%）<sup>3</sup>万；',
        '经过<i>x</i>年 人口约为141 178（1+1%）<i><sup>x</sup></i>万.'

      ]
    };
  },
  mounted() { },
  methods: {},
  methods: {
    openDialog(queryData) {
      this.thinkData = queryData
      this.thinkingDialog = !this.thinkingDialog
    },
    closeDialog() {
      this.showIndex = 0
    },
    changeNext() {
      if (this.showIndex < this.thinkData.length - 1) this.showIndex = this.showIndex + 1
    }
  },
};
</script>

<style lang="less" scoped></style>
<style lang="less" scoped>
li {
  list-style: none;
}
</style>

 src/books/mathBook/view/components/chapter005.vue

@@ -174,17 +174,38 @@
          <p>
            <span class="zt-ls"><b>例1</b></span>　在平面直角坐标系中，分别画出下列各角，并指出它们是第几象限角.
          </p>
          <p class="center">
            <img class="img-c" alt="" src="../../assets/images/0168-1.jpg" />
          <p class="p-btn" >
            <span>（1） 225°；</span>
            <span class="btn-box" @click="hadleAnswer(0)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="img">图5-4</p>
          <p>（1） 225°；（2） -300°.</p>
          <p class="p-btn" >
            <span>（2） -300°.</span>
            <span class="btn-box" @click="hadleAnswer(1)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer0" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1）
            以<i>x</i>轴的非负半轴为始边，逆时针方向旋转225°，即形成225°角，如图5-4（1）
            所示.因为225°角的终边在第三象限内，所以225°角是第三象限角.
          </p>
          <p>
            <p class="center">
              <img class="img-c" alt="" src="../../assets/images/0168-1.jpg" />
            </p>
            <p class="img">图5-4</p>
          </div>
          <p v-if="isShowAnswer1" >
            （2）
            以<i>x</i>轴的非负半轴为始边，顺时针方向旋转300°，即形成-300°角，如图5-4（2）
            所示.因为-300°角的终边在第一象限内，所以-300°角是第一象限角.
@@ -256,24 +277,81 @@
          <p>
            <span class="zt-ls"><b>例1</b></span>　在0°～360°内，找出与下列各角终边相同的角，并分别判断它们是第几象限角.
          </p>
          <p>（1） 600°；（2） -230°；（3） -890°.</p>
          <p>
          <p class="p-btn" >
            <span>（1） 600°；</span>
            <span class="btn-box" @click="hadleAnswer(2)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（2） -230°；</span>
            <span class="btn-box" @click="hadleAnswer(3)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（3） -890°.</span>
            <span class="btn-box" @click="hadleAnswer(4)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p v-if="isShowAnswer2" >
            <span class="zt-ls"><b>解</b></span>（1） 因为600°=240°+360°，所以600°角与240°角终边相同，是第三象限角.
          </p>
          <p>
          <p v-if="isShowAnswer3" >
            （2）
            因为-230°=130°-360°，所以-230°角与130°角终边相同，是第二象限角.
          </p>
          <p>
          <p v-if="isShowAnswer4" >
            （3）
            因为-890°=190°-3×360°，所以-890°角与190°角终边相同，是第三象限角.
          </p>
          <p>
            <span class="zt-ls"><b>例2</b></span>　写出下列角的集合.
          </p>
          <p>（1） 终边在<i>y</i>轴正半轴上的角的集合；</p>
          <p>（2） 终边在<i>y</i>轴负半轴上的角的集合；</p>
          <p>（3） 终边在<i>y</i>轴上的角的集合.</p>
          <p class="p-btn" >
            <span>（1） 终边在<i>y</i>轴正半轴上的角的集合；</span>
            <span class="btn-box" @click="hadleAnswer(5)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（2） 终边在<i>y</i>轴负半轴上的角的集合；</span>
            <span class="btn-box" @click="hadleAnswer(6)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（3） 终边在<i>y</i>轴上的角的集合.</span>
            <span class="btn-box" @click="hadleAnswer(7)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer5" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 在0°～360°内，终边在<i>y</i>轴正半轴上的角是90°角，
          </p>
@@ -281,11 +359,25 @@
          <p class="center">
            <i>S</i>1={<i>β</i>|<i>β</i>=90°+<i>k</i>·360°，<i>k</i>∈<b>Z</b>}.
          </p>
          </div>
          <div v-if="isShowAnswer6" > 
          <p>（2） 在0°～360°内，终边在<i>y</i>轴负半轴上的角是270°角，</p>
          <p>所以，终边在<i>y</i>轴负半轴上的角的集合是</p>
          <p class="center">
            <i>S</i>2={<i>β</i>|<i>β</i>=270°+<i>k</i>·360°，<i>k</i>∈<b>Z</b>}.
          </p>
          </div>
          <div v-if="isShowAnswer7" > 
            <p>（3） 终边在<i>y</i>轴上的角的集合是</p>
            <p><i>S</i>=<i>S</i><sub>1</sub>∪<i>S</i><sub>2</sub></p>
            <p>
              ={<i>β</i>|<i>β</i>=90°+<i>k</i>·360°，<i>k</i>∈<b>Z</b>}∪{<i>β</i>|<i>β</i>=270°+<i>k</i>·360°，<i>k</i>∈<b>Z</b>}
            </p>
            <p>
              ={<i>β</i>|<i>β</i>=90°+2<i>k</i>·180°，<i>k</i>∈<b>Z</b>}∪{<i>β</i>|<i>β</i>=90°+（2<i>k</i>+1）·180°，<i>k</i>∈<b>Z</b>}
            </p>
            <p>={<i>β</i>|<i>β</i>=90°+<i>m</i>·180°，<i>m</i>∈<b>Z</b>}.</p>
          </div>
        </div>
      </div>
    </div>
@@ -298,15 +390,7 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p>（3） 终边在<i>y</i>轴上的角的集合是</p>
          <p><i>S</i>=<i>S</i><sub>1</sub>∪<i>S</i><sub>2</sub></p>
          <p>
            ={<i>β</i>|<i>β</i>=90°+<i>k</i>·360°，<i>k</i>∈<b>Z</b>}∪{<i>β</i>|<i>β</i>=270°+<i>k</i>·360°，<i>k</i>∈<b>Z</b>}
          </p>
          <p>
            ={<i>β</i>|<i>β</i>=90°+2<i>k</i>·180°，<i>k</i>∈<b>Z</b>}∪{<i>β</i>|<i>β</i>=90°+（2<i>k</i>+1）·180°，<i>k</i>∈<b>Z</b>}
          </p>
          <p>={<i>β</i>|<i>β</i>=90°+<i>m</i>·180°，<i>m</i>∈<b>Z</b>}.</p>

          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -328,7 +412,6 @@
            <p><span>161</span></p>
          </li>
        </ul>

        <div class="padding-116">
          <h3 id="c050">习题5.1<span class="fontsz2">＞＞＞</span></h3>
          <div class="bj">
@@ -572,10 +655,18 @@
            <img class="img-c" alt="" src="../../assets/images/0174-6.jpg" />
          </p>
          <p class="img">图5-8</p>
          <p>
            <span class="zt-ls"><b>例1</b></span>　把下列各角化为弧度.
          <p class="p-btn" >
            <span><span class="zt-ls"><b>例1</b></span>　把下列各角化为弧度.</span>
            <span class="btn-box" @click="hadleAnswer(8)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>（1） 30°；（2） -225°；（3） 0°.</p>
          <div v-if="isShowAnswer8" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -654,8 +745,16 @@
              <mo>.</mo>
            </math>
          </p>
          <p>
            <span class="zt-ls"><b>例2</b></span>　把下列各角化为角度.
          </div>
          <p class="p-btn" >
            <span><span class="zt-ls"><b>例2</b></span>　把下列各角化为角度.</span>
            <span class="btn-box" @click="hadleAnswer(9)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （1）
@@ -669,6 +768,7 @@
              </mfrac>
            </math>；（2） 5rad（结果精确到0.01）.
          </p>
          <div v-if="isShowAnswer9" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -733,7 +833,8 @@
              <mo>.</mo>
            </math>
          </p>
          <div class="bk">
          </div>
          <div class="bk mt-60">
            <div class="bj1">
              <p class="left">
                <img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
@@ -758,7 +859,17 @@
          <p>
            <span class="zt-ls"><b>例3</b></span>　利用科学计算器，把下列各角进行弧度与角度的互化.（结果精确到0.01）
          </p>
          <p>（1） -5.6；（2） 154°13′.</p>
          <p class="p-btn" >
            <span>（1） -5.6；</span>
            <span class="btn-box" @click="hadleAnswer(10)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer10" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1）
            先将科学计算器的精确度设置为0.01，再将科学计算器设置为角度计算模式，科学计算器Ⅰ按<img class="inline" alt=""
@@ -773,6 +884,18 @@
            <img class="img-c" alt="" src="../../assets/images/0175-4.jpg" />
          </p>
          <p>所以　-5.6 <i>rad</i> ≈-320.86°.</p>
          </div>
          <p class="p-btn" >
            <span>（2） 154°13′.</span>
            <span class="btn-box" @click="hadleAnswer(11)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer11" > 
          <p>
            （2）
            先将科学计算器的精确度设置为0.01，再将科学计算器设置为弧度计算模式，科学计算器Ⅰ按<img class="inline" alt=""
@@ -787,6 +910,8 @@
            <img class="img-c" alt="" src="../../assets/images/0175-8.jpg" />
          </p>
          <p>所以　154°13′≈2.69 rad.</p>
          </div>
          <calculator />
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -992,7 +1117,8 @@
          <p class="center">
            <img class="img-d" alt="" src="../../assets/images/0176-11.jpg" />
          </p>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例1</b></span>　截至2021年4月，中国高速公路总里程约为16万千米，位居全球第一.某高速公路转弯处为一弧形高架桥，测得此处公路中线的总长为1
            200 m，该弧形高架桥所对应的圆心角为<math display="0">
              <mfrac>
@@ -1003,7 +1129,16 @@
                <mn>5</mn>
              </mfrac>
            </math>，求该弧形高架桥的转弯半径（结果精确到1 m）.
            </span>
            <span class="btn-box" @click="hadleAnswer(12)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer12" > 
          <p>
            <span class="zt-ls"><b>解</b></span> 由题意可知，<i>l</i>=1
            200，<math display="0">
@@ -1067,6 +1202,7 @@
        </div>
      </div>
    </div>
    </div>
    <!-- 166 -->
    <div class="page-box" page="173">
      <div v-if="showPageList.indexOf(173) > -1">
@@ -1080,11 +1216,21 @@
            <img class="img-c" alt="" src="../../assets/images/0177-1.jpg" />
          </p>
          <p class="img">图5-10</p>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例2</b></span>　如图5-10所示，要在一块废铁皮上剪出一个扇形，用于制作一个圆锥筒，要求这个扇形的圆心角为60°，半径为90
            cm .请求出这个扇形的弧长与面积.（结果分别精确到0.01 cm和0.01
            cm<sup>2</sup>）
            </span>
            <span class="btn-box" @click="hadleAnswer(13)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer13" > 
          <p>
            <span class="zt-ls"><b>解</b></span> 由于<math display="0">
              <msup>
@@ -1173,6 +1319,7 @@
          <p>
            所以，这个扇形的弧长约为94.26 cm，面积约为4 241.70 cm<sup>2</sup>.
          </p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -1509,7 +1656,6 @@
        </div>
      </div>
    </div>

    <!-- 169 -->
    <div class="page-box" page="176">
      <div v-if="showPageList.indexOf(176) > -1">
@@ -1522,14 +1668,24 @@
          </li>
        </ul>
        <div class="padding-116">
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例1</b></span>　如图5-14所示，已知<i>α</i>的终边经过点 <i>P</i>（3，-4），
            求sin<i>α</i>，cos<i>α</i>，tan<i>α</i>的值.
            </span>
            <span class="btn-box" @click="hadleAnswer(14)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="center">
            <img class="img-c" alt="" src="../../assets/images/0180-3.jpg" />
          </p>
          <p class="img">图5-14</p>
          <div v-if="isShowAnswer36" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
            由已知有<i>x</i>=3，<i>y</i>=-4，
@@ -1621,6 +1777,7 @@
              </mtr>
            </mtable>
          </math>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -1650,7 +1807,6 @@
        </div>
      </div>
    </div>

    <!-- 170 -->
    <div class="page-box" page="177">
      <div v-if="showPageList.indexOf(177) > -1">
@@ -1754,8 +1910,29 @@
          <p>
            <span class="zt-ls"><b>例2</b></span>　确定下列各三角函数值的符号.
          </p>
          <p>
            （1） sin（-210°）；（2） tan760°；（3）
          <p class="p-btn" >
            <span>（1） sin（-210°）；</span>
            <span class="btn-box" @click="hadleAnswer(15)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（2） tan760°；</span>
            <span class="btn-box" @click="hadleAnswer(16)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （3）
            <math display="0">
              <mi>cos</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
@@ -1767,16 +1944,29 @@
                <mn>12</mn>
              </mfrac>
            </math>.
            </span>
            <span class="btn-box" @click="hadleAnswer(17)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer15" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 因为-210°是第二象限角，所以
          </p>
          <p class="center">sin（-210°）＞0.</p>
          </div>
          <div v-if="isShowAnswer16" > 
          <p>
            （2）
            因为760°=40°+2×360°，可知760°角与40°角的终边相同，是第一象限角，所以
          </p>
          <p class="center">tan 760°＞0.</p>
          </div>
          <div v-if="isShowAnswer17" > 
          <p>
            （3） 由<math display="0">
              <mfrac>
@@ -1840,10 +2030,20 @@
            <mo>&lt;</mo>
            <mn>0</mn>
          </math>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例3</b></span>　根据sin <i>α</i>＞0，且cos <i>α</i>＜0，确定<i>α</i>是第几象限角.
            </span>
            <span class="btn-box" @click="hadleAnswer(18)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
          <p v-if="isShowAnswer18">
            <span class="zt-ls"><b>解</b></span> 因为sin
            <i>α</i>＞0，所以<i>α</i>的终边在第一或第二象限或<i>y</i>轴的正半轴上；又因为cos<i>α</i>＜0，所以<i>α</i>的终边在第二或第三象限或<i>x</i>轴的负半轴上.因此，<i>α</i>为第二象限角.
          </p>
@@ -1960,20 +2160,34 @@
            <p>第五单元 三角函数</p>
          </li>
          <li>
            <p><span>173</span></p>
            <p><span>173-174</span></p>
          </li>
        </ul>
        <div class="padding-116">
          <p>
            <span class="zt-ls"><b>例4</b></span>　求5sin180°-4sin90°+2tan180°-7sin270°的值.
          </p>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例4</b></span>　求5sin180°-4sin90°+2tan180°-7sin270°的值.
            </span>
            <span class="btn-box" @click="hadleAnswer(19)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer19" > 
          <p>
            <span class="zt-ls"><b>解</b></span> 5sin 180°-4sin 90°+2 tan
            180°-7sin 270°
          </p>
          <p>=5×0-4×1+2×0-7×（-1）</p>
          <p>=3.</p>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例5</b></span>　求<math display="0">
              <mi>sin</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
@@ -2003,7 +2217,17 @@
                <mn>2</mn>
              </mfrac>
            </math>的值.
            </span>
            <span class="btn-box" @click="hadleAnswer(20)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer20" > 

          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -2082,6 +2306,7 @@
              </mtable>
            </math>
          </p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -2144,10 +2369,8 @@
        </div>
      </div>
    </div>

    <!-- 174 -->
    <div class="page-box hidePage" page="181"></div>

    <!-- 175 -->
    <div class="page-box" page="182">
      <div v-if="showPageList.indexOf(182) > -1">
@@ -2156,7 +2379,7 @@
            <p>第五单元 三角函数</p>
          </li>
          <li>
            <p><span>175</span></p>
            <p><span>175-176</span></p>
          </li>
        </ul>
        <div class="padding-116">
@@ -2229,7 +2452,8 @@
              </mfrac>
            </math>.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例1</b></span>　已知<math display="0">
              <mi>cos</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
@@ -2240,7 +2464,16 @@
                <mn>5</mn>
              </mfrac>
            </math>， 且<i>α</i>是第四象限角，求sin<i>α</i>，tan<i>α</i>的值.
            </span>
            <span class="btn-box" @click="hadleAnswer(21)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer21" > 
          <p>
            <span class="zt-ls"><b>解</b></span> 因为
            <i>α</i>是第四象限角，所以sin<i>α</i>＜0 .
@@ -2337,6 +2570,7 @@
              </mtr>
            </mtable>
          </math>
          </div>
          <div class="bk">
            <div class="bj1">
              <p class="left">
@@ -2382,7 +2616,8 @@
              </math>.其开方后的符号是由正弦值的象限符号来确定的.同理，开方后余弦值的符号也一样.
            </p>
          </div>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例2</b></span>　已知<math display="0">
              <mi>tan</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
@@ -2393,7 +2628,16 @@
                <mn>5</mn>
              </mfrac>
            </math>，且<i>α</i>是第三象限角，求sin <i>α</i>，cos <i>α</i>的值.
            </span>
            <span class="btn-box" @click="hadleAnswer(22)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer22" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -2551,19 +2795,6 @@
              </mfrac>
            </math>.
          </p>
        </div>
      </div>
    </div>

    <!-- 176 -->
    <div class="page-box" page="183">
      <div v-if="showPageList.indexOf(183) > -1">
        <ul class="page-header-odd fl al-end">
          <li>176</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p>
            把<math display="0">
              <mi>cos</mi>
@@ -2612,10 +2843,21 @@
            </mfrac>
            <mo>.</mo>
          </math>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例3</b></span>　求证sin<sup>4</sup><i>α</i>-cos<sup>4</sup><i>α</i>=2sin
            <sup>2</sup><i>α</i>-1.
            </span>
            <span class="btn-box" @click="hadleAnswer(23)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer23" > 
          <p>
            <b>证明</b> sin<sup>4</sup><i>α</i>-cos<sup>4</sup><i>α</i>=（sin
            <sup>2</sup><i>α</i>+cos<sup>2</sup><i>α</i>）（sin<sup>2</sup><i>α</i>-cos<sup>2</sup><i>α</i>）
@@ -2623,7 +2865,9 @@
          <p>=sin<sup>2</sup><i>α</i>-cos<sup>2</sup><i>α</i></p>
          <p>=sin<sup>2</sup><i>α</i>-（1-sin<sup>2</sup><i>α</i>）</p>
          <p>=2sin<sup>2</sup><i>α</i>-1.</p>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例4</b></span>　化简<math display="0">
              <mfrac>
                <mrow>
@@ -2644,7 +2888,16 @@
                </mrow>
              </mfrac>
            </math>.
            </span>
            <span class="btn-box" @click="hadleAnswer(24)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer24" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -2778,7 +3031,8 @@
              </mtr>
            </mtable>
          </math>
          <div class="bk">
          </div>
          <div class="bk mt-60">
            <div class="bj1">
              <p class="left">
                <img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
@@ -2788,7 +3042,8 @@
              方法一的运算思路是由正弦函数、余弦函数变化为正切函数求出结果，我们简称为“弦化切”；方法二的运算思路是由正切函数变化为正弦函数和余弦函数的关系后求出结果，我们简称为“切化弦”.
            </p>
          </div>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例5</b></span>　已知tan<i>θ</i>=-3，求<math display="0">
              <mfrac>
                <mrow>
@@ -2815,7 +3070,16 @@
                </mrow>
              </mfrac>
            </math>的值.
            </span>
            <span class="btn-box" @click="hadleAnswer(25)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer25" > 
          <p>
            <span class="zt-ls"><b>解</b></span> 方法一：显然cos <i>θ</i>≠0，
          </p>
@@ -3097,7 +3361,10 @@
        </div>
      </div>
    </div>

    </div>
    <!-- 176 -->
    <div class="page-box hidePage" page="183">
    </div>
    <!-- 177 -->
    <div class="page-box" page="184">
      <div v-if="showPageList.indexOf(184) > -1">
@@ -3125,7 +3392,6 @@
        </div>
      </div>
    </div>

    <!-- 178 -->
    <div class="page-box" page="185">
      <div v-if="showPageList.indexOf(185) > -1">
@@ -3298,7 +3564,6 @@
        </div>
      </div>
    </div>

    <!-- 179 -->
    <div class="page-box" page="186">
      <div v-if="showPageList.indexOf(186) > -1">
@@ -3310,10 +3575,16 @@
            <p><span>179</span></p>
          </li>
        </ul>

        <div class="padding-116">
          <p>
            <span class="zt-ls"><b>例1</b></span>　求下列三角函数的值.
          <p class="p-btn" >
            <span><span class="zt-ls"><b>例1</b></span>　求下列三角函数的值.</span>
            <span class="btn-box" @click="hadleAnswer(26)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （1）
@@ -3345,6 +3616,7 @@
              </mrow>
            </math>；（3） tan 405°.
          </p>
          <div v-if="isShowAnswer26" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1）<math display="0">
              <mi>sin</mi>
@@ -3430,6 +3702,7 @@
            </math>；
          </p>
          <p>（3） tan405°=tan（45°+360°）=tan45°=1.</p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -3696,8 +3969,15 @@
          </li>
        </ul>
        <div class="padding-116">
          <p>
            <span class="zt-ls"><b>例2</b></span>　求下列三角函数的值.
          <p class="p-btn" >
            <span><span class="zt-ls"><b>例2</b></span>　求下列三角函数的值. </span>
            <span class="btn-box" @click="hadleAnswer(27)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （1） sin 225°；（2）
@@ -3713,6 +3993,7 @@
              </mfrac>
            </math>；（3） tan 570°.
          </p>
          <div v-if="isShowAnswer27" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1）<math display="0">
              <mi>sin</mi>
@@ -3897,6 +4178,7 @@
              </mtable>
            </math>
          </p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -4113,8 +4395,15 @@
              利用公式三，可以把负角的三角函数转化为正角的三角函数.
            </p>
          </div>
          <p>
            <span class="zt-ls"><b>例3</b></span>　求下列三角函数的值.
          <p class="p-btn" >
            <span><span class="zt-ls"><b>例3</b></span>　求下列三角函数的值.</span>
            <span class="btn-box" @click="hadleAnswer(28)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （1） sin（-45°）；（2） cos（-390°）；（3）
@@ -4133,6 +4422,7 @@
              <mo stretchy="false">)</mo>
            </math>.
          </p>
          <div v-if="isShowAnswer28" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -4343,6 +4633,7 @@
        </div>
      </div>
    </div>
    </div>
    <!-- 183  -->
    <div class="page-box" page="190">
      <div v-if="showPageList.indexOf(190) > -1">
@@ -4458,8 +4749,15 @@
          <p>
            公式一至公式四统称为三角函数的诱导公式.利用这些公式可以把任意角的三角函数转化为锐角三角函数.
          </p>
          <p>
            <span class="zt-ls"><b>例4</b></span>　求下列三角函数的值.
          <p class="p-btn" >
            <span><span class="zt-ls"><b>例4</b></span>　求下列三角函数的值.</span>
            <span class="btn-box" @click="hadleAnswer(29)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （1） cos 135°；（2）
@@ -4486,6 +4784,7 @@
              </mfrac>
            </math>.
          </p>
          <div v-if="isShowAnswer29" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -4680,7 +4979,9 @@
              <mo>.</mo>
            </math>
          </p>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例5</b></span>　化简：<math display="0">
              <mfrac>
                <mrow>
@@ -4732,7 +5033,16 @@
                </mrow>
              </mfrac>
            </math>
            </span>
            <span class="btn-box" @click="hadleAnswer(30)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer30" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
          </p>
@@ -4853,6 +5163,7 @@
              </mtable>
            </math>
          </p>
          </div>
          <p><b>归纳总结</b></p>
          <p>
            利用诱导公式，把任意角的三角函数值转化为锐角的三角函数值的一般步骤为：
@@ -4871,7 +5182,7 @@
            <p>第五单元 三角函数</p>
          </li>
          <li>
            <p><span>185</span></p>
            <p><span>185-186</span></p>
          </li>
        </ul>
        <div class="padding-116">
@@ -4905,47 +5216,17 @@
          <p>
            <span class="zt-ls"><b>例6</b></span>　利用科学计算器计算.（结果精确到0.01）
          </p>
          <p>
            （1） sin 63°52′41″；（2）<math display="0">
              <mi>cos</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
              <mfrac>
                <mrow>
                  <mn>4</mn>
                  <mi>π</mi>
                </mrow>
                <mn>3</mn>
              </mfrac>
            </math>；（3）
            <math display="0">
              <mi>tan</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mo>−</mo>
                <mfrac>
                  <mrow>
                    <mn>6</mn>
                    <mi>π</mi>
                  </mrow>
                  <mn>5</mn>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>.
          <p class="p-btn" >
            <span>（1） sin 63°52′41″；</span>
            <span class="btn-box" @click="hadleAnswer(31)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
        </div>
      </div>
    </div>
    <!-- 186 -->
    <div class="page-box" page="193">
      <div v-if="showPageList.indexOf(193) > -1">
        <ul class="page-header-odd fl al-end">
          <li>186</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <div v-if="isShowAnswer31" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1）
            先将精确度设置为0.01，再将科学计算器设置为角度计算模式，然后依次按下列各键：
@@ -4958,6 +5239,30 @@
            <img class="img-c" alt="" src="../../assets/images/0197-2.jpg" />
          </p>
          <p>所以 sin 63°52′41″≈0.90.</p>
          </div>
          <p class="p-btn" >
            <span>
              （2）<math display="0">
                <mi>cos</mi>
                <mo data-mjx-texclass="NONE">⁡</mo>
                <mfrac>
                  <mrow>
                    <mn>4</mn>
                    <mi>π</mi>
                  </mrow>
                  <mn>3</mn>
                </mfrac>
              </math>；
            </span>
            <span class="btn-box" @click="hadleAnswer(32)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer32" > 
          <p>
            （2）
            先将精确度设置为0.01，再将科学计算器设置为弧度计算模式，然后依次按下列各键：
@@ -4987,6 +5292,36 @@
              <mo>.</mo>
            </math>
          </p>
          </div>
          <p class="p-btn" >
            <span>
              （3）
              <math display="0">
                <mi>tan</mi>
                <mo data-mjx-texclass="NONE">⁡</mo>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mrow>
                      <mn>6</mn>
                      <mi>π</mi>
                    </mrow>
                    <mn>5</mn>
                  </mfrac>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>.
            </span>
            <span class="btn-box" @click="hadleAnswer(33)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer33" > 
          <p>
            （3）
            先将精确度设置为0.01，再将科学计算器设置为弧度计算模式，然后依次按下列各键：
@@ -5020,6 +5355,7 @@
              <mo>.</mo>
            </math>
          </p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -5029,6 +5365,9 @@
          </div>
        </div>
      </div>
    </div>
    <!-- 186 -->
    <div class="page-box hidePage" page="193">
    </div>
    <!-- 187 -->
    <div class="page-box" page="194">
@@ -5230,7 +5569,19 @@
          <p>
            <span class="zt-ls"><b>例1</b></span>　用“五点法”画出下列函数在区间［0，2π］内的简图.
          </p>
          <p>（1） <i>y</i>=-sin<i>x</i>；（2） <i>y</i>=1+sin<i>x</i>.</p>
          <p class="p-btn" >
            <span>
              （1） <i>y</i>=-sin<i>x</i>；
            </span>
            <span class="btn-box" @click="hadleAnswer(34)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer34" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 列表（表5-6）.
          </p>
@@ -5245,6 +5596,18 @@
            <img class="img-d" alt="" src="../../assets/images/0201-3.jpg" />
          </p>
          <p class="img">图5-27</p>
          </div>
          <p class="p-btn" >
            <span>（2） <i>y</i>=1+sin<i>x</i>.</span>
            <span class="btn-box" @click="hadleAnswer(35)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer35" > 
          <p>（2） 列表（表5-7）.</p>
          <p class="img">表5-7</p>
          <p class="center">
@@ -5257,6 +5620,8 @@
            <img class="img-d" alt="" src="../../assets/images/0201-5.jpg" />
          </p>
          <p class="img">图5-28</p>
          </div>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
        </div>
      </div>
    </div>
@@ -5371,7 +5736,8 @@
          <p>
            因为sin（-<i>x</i>）=-sin<i>x</i>，所以<i>y</i>=sin<i>x</i>是奇函数，其图像关于原点对称.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例1</b></span>　已知<math display="0">
              <mi>sin</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
@@ -5386,7 +5752,16 @@
                <mn>2</mn>
              </mfrac>
            </math>，求<i>a</i>的取值范围.
            </span>
            <span class="btn-box" @click="hadleAnswer(36)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer36" > 
          <p>
            <span class="zt-ls"><b>解</b></span> 因为　-1≤sin<i>x</i>≤1，
          </p>
@@ -5408,10 +5783,35 @@
            </math>，
          </p>
          <p>解得　1≤<i>a</i>≤5.</p>
          </div>
          <p>
            <span class="zt-ls"><b>例2</b></span>　求使下列函数取得最大值、最小值的<i>x</i>的集合，并求出这些函数的最大值、最小值.
          </p>
          <p>（1） <i>y</i>=3+sin<i>x</i>；（2） <i>y</i>=-2sin<i>x</i>.</p>
          <p class="p-btn" >
            <span>
              （1） <i>y</i>=3+sin<i>x</i>；
            </span>
            <span class="btn-box" @click="hadleAnswer(37)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2） <i>y</i>=-2sin<i>x</i>.
            </span>
            <span class="btn-box" @click="hadleAnswer(38)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer37" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1）
            使函数<i>y</i>=3+sin<i>x</i>取得最大值的<i>x</i>的集合，就是使函数<i>y</i>=sin<i>x</i>取得最大值的<i>x</i>的集合<math display="0">
@@ -5477,6 +5877,8 @@
              </mrow>
            </math>.这时函数<i>y</i>=3+sin<i>x</i>的最小值为<i>y</i>=3+（-1）=2.
          </p>
          </div>
          <div v-if="isShowAnswer38" > 
          <p>
            （2）
            使函数<i>y</i>=-2sin<i>x</i>取得最大值的<i>x</i>的集合，就是使函数<i>y</i>=sin<i>x</i>取得最小值的<i>x</i>的集合<math display="0">
@@ -5542,6 +5944,7 @@
              </mrow>
            </math>.这时函数<i>y</i>=-2sin<i>x</i>的最小值为<i>y</i>=-2×1=-2.
          </p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -5666,7 +6069,8 @@
          <p>
            <b>例</b> 不求值，利用正弦函数的单调性，比较下列各对正弦值的大小.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            （1）<math display="0">
              <mi>sin</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
@@ -5687,7 +6091,19 @@
                </mrow>
                <mn>3</mn>
              </mfrac>
            </math>；（2）<math display="0">
              </math>；
            </span>
            <span class="btn-box" @click="hadleAnswer(39)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2）<math display="0">
              <mi>sin</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
              <mrow data-mjx-texclass="INNER">
@@ -5712,7 +6128,16 @@
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>.
            </span>
            <span class="btn-box" @click="hadleAnswer(40)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer39" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 因为　<math display="0">
              <mfrac>
@@ -5788,21 +6213,7 @@
            <mtext>.&nbsp;</mtext>
          </math>
        </div>
      </div>
    </div>

    <!-- 193 -->
    <div class="page-box hidePage" page="200"></div>

    <!-- 194 -->
    <div class="page-box" page="201">
      <div v-if="showPageList.indexOf(201) > -1">
        <ul class="page-header-odd fl al-end">
          <li>194</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <div v-if="isShowAnswer40" > 
          <p>
            （2） 因为　<math display="0">
              <mo>−</mo>
@@ -5866,6 +6277,23 @@
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
          </math>
          </div>
        </div>
      </div>
    </div>

    <!-- 193 -->
    <div class="page-box hidePage" page="200"></div>

    <!-- 194 -->
    <div class="page-box" page="201">
      <div v-if="showPageList.indexOf(201) > -1">
        <ul class="page-header-odd fl al-end">
          <li>194</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -6022,7 +6450,28 @@
            <p class="img">图5-32</p>
          </div>
          <p><b>例</b> 用“五点法”画出下列函数在区间［0，2π］内的简图.</p>
          <p>（1） <i>y</i>=2cos <i>x</i>；（2） <i>y</i>=-1+cos <i>x</i>.</p>
          <p class="p-btn" >
            <span>（1） <i>y</i>=2cos <i>x</i>；</span>
            <span class="btn-box" @click="hadleAnswer(41)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（2） <i>y</i>=-1+cos <i>x</i>.</span>
            <span class="btn-box" @click="hadleAnswer(42)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <div v-if="isShowAnswer41" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 列表（表5-10）.
          </p>
@@ -6036,6 +6485,22 @@
          <p class="img">图5-33</p>
          <p>描点连线得<i>y</i>=2cos <i>x</i>在区间［0，2π］</p>
          <p>内的简图，如图5-33所示.</p>
          </div>
          <div v-if="isShowAnswer42" > 
            <p>（2） 列表（表5-11）.</p>
            <p class="img">表5-11</p>
            <p class="center">
              <img class="img-a" alt="" src="../../assets/images/0208-1.jpg" />
            </p>
            <p>
              描点连线得<i>y</i>=-1+cos
              <i>x</i>在区间［0，2π］内的简图，如图5-34所示.
            </p>
            <p class="center">
              <img class="img-d" alt="" src="../../assets/images/0208-2.jpg" />
            </p>
            <p class="img">图5-34</p>
          </div>
        </div>
      </div>
    </div>
@@ -6051,19 +6516,7 @@
          </li>
        </ul>
        <div class="padding-116">
          <p>（2） 列表（表5-11）.</p>
          <p class="img">表5-11</p>
          <p class="center">
            <img class="img-a" alt="" src="../../assets/images/0208-1.jpg" />
          </p>
          <p>
            描点连线得<i>y</i>=-1+cos
            <i>x</i>在区间［0，2π］内的简图，如图5-34所示.
          </p>
          <p class="center">
            <img class="img-d" alt="" src="../../assets/images/0208-2.jpg" />
          </p>
          <p class="img">图5-34</p>

          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -6144,9 +6597,17 @@
            余弦函数<i>y</i>=cos
            <i>x</i>在每一个区间［2<i>k</i>π，2<i>k</i>π+π］（<i>k</i>∈<b>Z</b>）上都是减函数，其值由1减小到-1；在每一个区间［2<i>k</i>π+π，2<i>k</i>π+2π］（<i>k</i>∈<b>Z</b>）上都是增函数，其值由-1增大到1.
          </p>
          <p>
            <span class="zt-ls"><b>例1</b></span>　求函数<i>y</i>=-1+cos <i>x</i>的最大值、最小值、最小正周期及值域.
          <p class="p-btn" >
            <span><span class="zt-ls"><b>例1</b></span>　求函数<i>y</i>=-1+cos <i>x</i>的最大值、最小值、最小正周期及值域.</span>
            <span class="btn-box" @click="hadleAnswer(43)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer43" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
            当<i>x</i>=2<i>k</i>π（<i>k</i>∈<b>Z</b>）时，函数<i>y</i>=-1+cos
@@ -6160,6 +6621,7 @@
            函数<i>y</i>=-1+cos <i>x</i>的最小正周期为2π；函数<i>y</i>=-1+cos
            <i>x</i>的值域为[-2，0].
          </p>
          </div>
        </div>
      </div>
    </div>
@@ -6187,7 +6649,8 @@
          <p>
            <span class="zt-ls"><b>例2</b></span>　不求值，利用余弦函数的单调性，比较下列各对余弦值的大小.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            （1）
            <math display="0">
              <mi>cos</mi>
@@ -6209,7 +6672,19 @@
                </mrow>
                <mn>4</mn>
              </mfrac>
            </math>；（2）
              </math>；
            </span>
            <span class="btn-box" @click="hadleAnswer(44)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>
              （2）
            <math display="0">
              <mi>cos</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
@@ -6235,7 +6710,16 @@
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>.
            </span>
            <span class="btn-box" @click="hadleAnswer(45)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer44" > 
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 因为<math display="0">
              <mi>π</mi>
@@ -6301,6 +6785,8 @@
            </mfrac>
            <mo>.</mo>
          </math>
          </div>
          <div v-if="isShowAnswer45" > 
          <p>
            （2）<math display="0">
              <mi>cos</mi>
@@ -6413,6 +6899,7 @@
            </mrow>
            <mo>.</mo>
          </math>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -6707,7 +7194,8 @@
              </mfrac>
            </math>.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例1</b></span>　已知<math display="0">
              <mi>cos</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
@@ -6721,8 +7209,16 @@
                <mn>2</mn>
              </mfrac>
            </math>，且<i>x</i>∈［0，2π］ ，求<i>x</i>的值.
            </span>
            <span class="btn-box" @click="hadleAnswer(46)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
          <p v-if="isShowAnswer46">
            <span class="zt-ls"><b>解</b></span> 因为<math display="0">
              <mi>cos</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
@@ -6835,7 +7331,8 @@
              </mfrac>
            </math>.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例2</b></span>　已知<math display="0">
              <mi>tan</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
@@ -6864,7 +7361,16 @@
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>，且0°≤<i>x</i>≤360°，求<i>x</i>的值.
            </span>
            <span class="btn-box" @click="hadleAnswer(47)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer47" > 
          <p>
            <span class="zt-ls"><b>解</b></span> 因为<math display="0">
              <mi>tan</mi>
@@ -6924,6 +7430,7 @@
          </p>
          <p>所以符合条件的第三象限角是<i>x</i>=180°+60°=240°.</p>
          <p>所以<i>x</i>=60°或<i>x</i>=240°.</p>
          </div>
          <div class="bk">
            <div class="bj1">
              <p class="left">
@@ -6942,7 +7449,8 @@
              根据<i>x</i>所在的象限和诱导公式，写出满足题目给定范围的<i>x</i>的值.
            </p>
          </div>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例3</b></span>　已知<math display="0">
              <mi>cos</mi>
              <mo data-mjx-texclass="NONE">⁡</mo>
@@ -6953,7 +7461,16 @@
                <mn>2</mn>
              </mfrac>
            </math>，且<i>x</i>∈［-π，π］，求<i>x</i>的值.
            </span>
            <span class="btn-box" @click="hadleAnswer(48)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer48" > 
          <p>
            <span class="zt-ls"><b>解</b></span> 因为<math display="0">
              <mi>cos</mi>
@@ -7048,6 +7565,7 @@
              </mfrac>
            </math>.
          </p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -7085,7 +7603,8 @@
          <p>
            根据已知特殊的三角函数值求角的方法，借助计算工具，可以解决已知任意三角函数值求角的问题.
          </p>
          <p>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例1</b></span>　已知<math display="0">
              <mi>α</mi>
              <mo>∈</mo>
@@ -7104,7 +7623,17 @@
                <mo data-mjx-texclass="CLOSE">]</mo>
              </mrow>
            </math>，求<i>α</i>的值.（结果精确到0.000 1）
            </span>
            <span class="btn-box" @click="hadleAnswer(49)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <calculator />
          <div v-if="isShowAnswer49" > 
          <p>
            <span class="zt-ls"><b>解</b></span> 因为<math display="0">
              <mi>α</mi>
@@ -7138,28 +7667,26 @@
            <img class="img-c" alt="" src="../../assets/images/0214-5.jpg" />
          </p>
          <p>所以　<i>α</i>≈1.233 6.</p>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例2</b></span>　已知cos <i>α</i>=0.694
            3，0°≤<i>α</i>≤180°，求<i>α</i>的值.（结果精确到0.000 1）
            </span>
            <span class="btn-box" @click="hadleAnswer(50)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer50" > 
          <p>
            <span class="zt-ls"><b>解</b></span>　因为0°≤<i>α</i>≤180°，所以<i>α</i>在<i>y</i>=cos
            <i>α</i>的一个单调区间内，这时使cos <i>α</i>=0.694
            3的角<i>α</i>的值是唯一的.
          </p>
        </div>
      </div>
    </div>
    <!-- 204 -->
    <div class="page-box" page="211">
      <div v-if="showPageList.indexOf(211) > -1">
        <ul class="page-header-odd fl al-end">
          <li>204</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>

        <div class="padding-116">
          <p>
            先将科学计算器的精确度设置为0.000
            1，再将科学计算器设置为角度计算模式，然后依次按键：
@@ -7176,7 +7703,21 @@
            注意：应当区分所给条件中角的单位是角度还是弧度.如果是角度，计算时应用角度计算模式；
            如果是弧度，计算时应用弧度计算模式.
          </p>
          <p>
          </div>
        </div>
      </div>
    </div>
    <!-- 204 -->
    <div class="page-box" page="211">
      <div v-if="showPageList.indexOf(211) > -1">
        <ul class="page-header-odd fl al-end">
          <li>204</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例3</b></span>　已知tan <i>α</i>=-2.747 0，<math display="0">
              <mi>α</mi>
              <mo>∈</mo>
@@ -7195,7 +7736,17 @@
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>，求<i>α</i>的值.（结果精确到0.000 1）
            </span>
            <span class="btn-box" @click="hadleAnswer(51)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <calculator />
          <div v-if="isShowAnswer51" > 
          <p>
            <span class="zt-ls"><b>解</b></span> 因为<math display="0">
              <mi>α</mi>
@@ -7229,15 +7780,28 @@
            <img class="img-c" alt="" src="../../assets/images/0215-6.jpg" />
          </p>
          <p>所以　<i>α</i>≈-1.221 7.</p>
          <p>
          </div>
          <p class="p-btn" >
            <span>
            <span class="zt-ls"><b>例4</b></span>　已知sin <i>α</i>=-0.857
            2，<i>α</i>∈［0，2π］，求<i>α</i>的值.（结果精确到0.000 1）
            </span>
            <span class="btn-box" @click="hadleAnswer(52)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
            <span class="btn-box" @click="openDialog(thinkOne)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="block">
            <span class="zt-ls2"><b>分析</b></span>　因为sin <i>α</i>=-0.857
            2＜0，在［0，2π］范围内有两个<i>α</i>值满足条件，它们分别位于第三象限和第四象限，即<i>α</i>在［π，2π］范围内.可用科学计算器先求出sin
            <i>α</i>=0.857 2所对应的锐角，再利用诱导公式求出所求的角.
          </p>
          <div v-if="isShowAnswer52" > 
          <p>
            <span class="zt-ls"><b>解</b></span>
            先将科学计算器的精确度设置为0.000
@@ -7250,6 +7814,19 @@
          <p class="center">
            <img class="img-c" alt="" src="../../assets/images/0215-8.jpg" />
          </p>
            <p>即</p>
            <p class="center">sin 1.029 8≈0.857 2.</p>
            <p>因为</p>
            <p class="center">sin（π+1.029 8）=-sin 1.029 8≈-0.857 2，</p>
            <p>所以符合条件的第三象限角是π+1.029 8≈4.171 4.</p>
            <p>因为</p>
            <p class="center">sin（2π-1.029 8）=-sin 1.029 8≈-0.857 2，</p>
            <p>所以符合条件的第四象限角是2π-1.029 8≈5.253 4.</p>
            <p>
              所以满足sin <i>α</i>=-0.857
              2，<i>α</i>∈［0，2π］的角<i>α</i>的集合为{4.171 4，5.253 4}.
            </p>
          </div>
        </div>
      </div>
    </div>
@@ -7265,18 +7842,6 @@
          </li>
        </ul>
        <div class="padding-116">
          <p>即</p>
          <p class="center">sin 1.029 8≈0.857 2.</p>
          <p>因为</p>
          <p class="center">sin（π+1.029 8）=-sin 1.029 8≈-0.857 2，</p>
          <p>所以符合条件的第三象限角是π+1.029 8≈4.171 4.</p>
          <p>因为</p>
          <p class="center">sin（2π-1.029 8）=-sin 1.029 8≈-0.857 2，</p>
          <p>所以符合条件的第四象限角是2π-1.029 8≈5.253 4.</p>
          <p>
            所以满足sin <i>α</i>=-0.857
            2，<i>α</i>∈［0，2π］的角<i>α</i>的集合为{4.171 4，5.253 4}.
          </p>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -7617,6 +8182,55 @@
    </div>
    <!-- 211 -->
    <div class="page-box hidePage" page="218"></div>
    <!-- 解题思路弹窗 -->
    <el-dialog :visible.sync="thinkingDialog" width="40%" :append-to-body="true" :show-close="false"
      @close="closeDialog" class="thinkDialog">
      <div slot="title" class="think-header"
        style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
        <span style=""> 分析 </span>
        <svg style="position: absolute; right:10px;cursor: pointer;" @click="thinkingDialog = false" t="1718596022986"
          class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
          height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
          <path
            d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
            fill="#979797" p-id="4253"></path>
          <path
            d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
            fill="#979797" p-id="4254"></path>
        </svg>
      </div>
      <ul>
        <li v-for="(item, index) in thinkData" :key="index">
          <div v-if="index <= showIndex" style="display: flex">
            <span style="position: relative">
              <span style="position: absolute; top: 16px; left: 13px; color: #fff">{{ index + 1 }}</span>
              <img src="../../assets/images/icon/blue-group.png" alt="" style="margin-right: 10px"
                v-if="index < thinkOne.length - 1" />
              <img src="../../assets/images/icon/blue.png" alt="" v-if="index == thinkOne.length - 1"
                style="margin-right: 10px" />
            </span>
            <p class="txt-p" v-html="item"></p>
          </div>
        </li>
      </ul>
      <div @click="changeNext" style="
          display: flex;
          flex-direction: column;
          align-items: center;
          justify-content: center;
        ">
        <img src="../../assets/images/icon/mouse.png" alt="" v-if="showIndex < thinkData.length - 1" />
        <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" t="1710234570135"
          class="icon" viewBox="0 0 1024 1024" version="1.1" p-id="5067" width="15" height="15">
          <path
            d="M2.257993 493.371555 415.470783 906.584344 512 1003.113561 608.529217 906.584344 1021.742007 493.371555 925.212789 396.842337 512 810.055127 98.787211 396.842337Z"
            fill="#1296db" p-id="5068" />
          <path
            d="M2.257993 117.980154 415.470783 531.192944 512 627.722161 608.529217 531.192944 1021.742007 117.980154 925.212789 21.450937 512 434.663727 98.787211 21.450937Z"
            fill="#1296db" p-id="5069" />
        </svg>
      </div>
    </el-dialog>
  </div>
</template>

@@ -7624,6 +8238,15 @@
import paint from '@/components/paint/index.vue'
import examinations from "@/components/examinations/index.vue";
import fillInTable from "@/components/fillInTable/index.vue";
import calculator from '@/components/calculator/index.vue'
const handleShow = (num) => {
  const obj = {}
  for (let index = 0; index < num; index++) {
    obj['isShowAnswer' + index] = false
  }
  return obj
}
const showObj = handleShow(60)
export default {
  name: "",
  props: {
@@ -7635,9 +8258,10 @@
      type: Object,
    },
  },
  components: { examinations, fillInTable,paint },
  components: { examinations, fillInTable,paint,calculator },
  data() {
    return {
      ...showObj,
      isShowAnswer:false,
      queryDataOne: {
        stemTxt:"完成下表，并利用“五点法”画出<i>y</i>=3sin <i>x</i>在区间［0，2π］内的简图，并说明<i>y</i>=3sin <i>x</i>的图像与正弦函数<i>y</i>=sin <i>x</i>的图像的区别和联系.",
@@ -7656,10 +8280,30 @@
          ["y=1-cosx", "", "", "", "", ""],
        ],
        answer:"<p>1,0,-1,0,1</p><p>0,1,2,1,0</p>"
      }

      },
      showIndex:0,
      thinkingDialog: false,
      thinkData:[],
      thinkOne:[
        '因为sin <i>α</i>=-0.8572＜0，在［0，2π］范围内有两个<i>α</i>值满足条件，它们分别位于第三象限和第四象限，即<i>α</i>在［π，2π］范围内.可用科学计算器先求出sin<i>α</i>=0.857 2所对应的锐角，再利用诱导公式求出所求的角.'
      ]
    }
  },
  methods:{
    hadleAnswer(index) {
      this['isShowAnswer' + index] = !this['isShowAnswer' + index]
    },
    openDialog(queryData) {
      this.thinkData = queryData
      this.thinkingDialog = !this.thinkingDialog
    },
    closeDialog() {
      this.showIndex = 0
    },
    changeNext() {
      if (this.showIndex < this.thinkData.length - 1) this.showIndex = this.showIndex + 1
    }
  }
}
</script>

@@ -7669,4 +8313,7 @@
  border: 1px solid #00adee;
  display: flex;
}
li {
  list-style: none;
}
</style>

 src/books/mathBook/view/components/index.vue

@@ -161,8 +161,8 @@
    }, 500);

    // 测试页面跳转
    setTimeout(() => {
      this.gotoPage(3, 76);
    // setTimeout(() => {
    //   this.gotoPage(5, 210);
    //   //   setTimeout(() => {
    //   //     this.renderSign("Highlight", {
    //   //       id: "2ACA9359",
@@ -190,7 +190,7 @@
    //   //   txt: " 运动系统是由骨、骨连结和骨骼肌三部分组成的。全身的骨通过骨连结组成人体骨骼（见图1-1）。骨骼是人体的支架，具有保护内脏器官、供肌肉附着和作为肌肉运动的杠杆等作用。在神经系统的支配下，肌肉收缩牵动所附着的骨绕着关节转动，使身体产生各种动作。所以，运动系统具有运动、支持和保护等功能，幼年时期的骨骼还具有造血功能。 ",
    //   //   txtIndex: 57
    //   // });
    }, 500);
    // }, 500);

    // 获取题目id列表
    this.getQuestionId();

 src/components/calculator/index.vue

New file
@@ -0,0 +1,58 @@
<template>
  <div ref="ggbContainer" class="ggb-container"></div>
</template>

<script lang="ts">

export default {
  mounted() {
  if (!window.GGBApplet) {
      const script = document.createElement("script");
      script.src = "https://www.geogebra.org/apps/deployggb.js";
      script.onload = () => {
        this.initGeoGebra();
      };
      document.body.appendChild(script);
    } else {
      this.initGeoGebra();
    }
  },
  methods:{
    initGeoGebra() {
        var params = {
          id: "ggbApplet",
          appName: "scientific",
          width: 600,
          height: 600,
          showToolBar: true,
          borderColor: null,
          showMenuBar: true,
          allowStyleBar: true,
          showAlgebraInput: true,
          enableLabelDrags: false,
          enableShiftDragZoom: true,
          capturingThreshold: null,
          showToolBarHelp: false,
          errorDialogsActive: true,
          showTutorialLink: true,
          showLogging: true,
          useBrowserForJS: false,
        };

        if (this.$refs.ggbContainer) {
          const applet = new GGBApplet(params, true);
          applet.inject(this.$refs.ggbContainer);
        }
      }
  }
}

</script>

<style scoped>
.ggb-container {
  width: 100%;
  height: 100%;
  /* 其他样式 */
}
</style>

 src/components/examinations/index.vue

@@ -567,6 +567,7 @@
  methods: {
    // 获取不受保护的图片
    getPublicImage(md5, width, height) {
      if(!md5) return 
      if(md5.includes('http')) return md5
      let src = null;
      if (md5) {