2024年成考专升本《高等数学一》每日一练试题08月06日

<p class="introTit">单选题</p><p>1、设y＝e^2x，则dy＝（）。</p><ul><li>A：e^2xdx</li><li>B：2e^2xdx</li><li>C：<img src='https://img2.meite.com/questions/202211/176375aebd68986.png' /></li><li>D：－2e^2xdx</li></ul><p>答 案：B</p><p>解 析：由复合函数的求导法则可知<img src="https://img2.meite.com/questions/202211/176375aed18ece4.png" />，故<img src="https://img2.meite.com/questions/202211/176375aee148158.png" />。</p><p>2、微分方程y'＋y＝0的通解为y＝（）。</p><ul><li>A：e^-x＋C</li><li>B：－e^-x＋C</li><li>C：Ce^-x</li><li>D：Ce^x</li></ul><p>答 案：C</p><p>解 析：所给方程为可分离变量方程，分离变量得<img src="https://img2.meite.com/questions/202212/01638868fa3de9e.png" />。两端分别积分<img src="https://img2.meite.com/questions/202212/01638869176a115.png" />。</p><p>3、设y＝x²，则<img src="https://img2.meite.com/questions/202211/166374928fecddc.png" />＝（）。</p><ul><li>A：x³</li><li>B：x</li><li>C：<img src='https://img2.meite.com/questions/202211/16637492a5b3940.png' /></li><li>D：2x</li></ul><p>答 案：D</p><p>解 析：<img src="https://img2.meite.com/questions/202211/16637492ad52674.png" />。</p><p class="introTit">主观题</p><p>1、设曲线x=√y、y＝2及x＝0所围成的平面图形为D．（1）求平面图形D的面积S。<br />（2）求平面图形D绕y轴旋转一周所生成旋转体的体积Vy。</p><p>答 案：解：D的图形见右图阴影部分。<img src="https://img2.meite.com/questions/202211/186376ee948d92a.png" />（1）由<img src="https://img2.meite.com/questions/202211/186376eeac047bd.png" />解得<img src="https://img2.meite.com/questions/202211/186376eec7a8197.png" />于是<img src="https://img2.meite.com/questions/202211/186376eeea6d7fd.png" /><br />（2）<img src="https://img2.meite.com/questions/202211/186376eefb038fe.png" /></p><p>2、设<img src="https://img2.meite.com/questions/202211/2963856c2de4338.png" />求C的值。</p><p>答 案：解：<img src="https://img2.meite.com/questions/202211/2963856c7163364.png" />则<img src="https://img2.meite.com/questions/202211/2963856cb44e6d7.png" />，有<img src="https://img2.meite.com/questions/202211/2963856cc277361.png" />，<img src="https://img2.meite.com/questions/202211/2963856cd1025c5.png" />。</p><p>3、计算<img src="https://img2.meite.com/questions/202109/1661429dcbbed55.png" width="107" /></p><p>答 案：<img src="https://img2.meite.com/questions/202109/1661429de15b12a.png" width="259" /></p><p class="introTit">填空题</p><p>1、设<img src="https://img2.meite.com/questions/202405/166645bc5723499.png" />，（t为参数），则<img src="https://img2.meite.com/questions/202405/166645bc5d4bb73.png" />（）  </p><p>答 案：3</p><p>解 析：<img src="https://img2.meite.com/questions/202405/166645bc64d94d1.png" /></p><p>2、曲线<img src="https://img2.meite.com/questions/202211/306386d334837c7.png" />的铅直渐近线方程为（）。</p><p>答 案：x＝2</p><p>解 析：因为<img src="https://img2.meite.com/questions/202211/306386d34bea9e7.png" />，故曲线的铅直线渐近线方程x＝2。</p><p>3、函数<img src="https://img2.meite.com/questions/202211/306386fad35365a.png" />在[1，2]上符合拉格朗日中值定理的<img src="https://img2.meite.com/questions/202211/306386fdd7622ab.png" />＝_。</p><p>答 案：<img src="https://img2.meite.com/questions/202211/306386fde85c879.png" /></p><p>解 析：由拉格朗日中值定理有<img src="https://img2.meite.com/questions/202211/306386fe2edc9ca.png" />解得<img src="https://img2.meite.com/questions/202211/306386fe47ab869.png" />，其中<img src="https://img2.meite.com/questions/202211/306386fdd7622ab.png" />＝－<img src="https://img2.meite.com/questions/202211/306386fde85c879.png" />（舍），得<img src="https://img2.meite.com/questions/202211/306386fdd7622ab.png" />＝<img src="https://img2.meite.com/questions/202211/306386fde85c879.png" />。</p><p class="introTit">简答题</p><p>1、计算<img src="https://img2.meite.com/questions/202303/036401a007c339a.png" />  </p><p>答 案：<img src="https://img2.meite.com/questions/202303/036401af3a8d76a.png" /></p>