2024年成考专升本《高等数学二》每日一练试题09月30日

<p class="introTit">判断题</p><p>1、若<img src="https://img2.meite.com/questions/202307/1364af5780970e6.png" />，则<img src="https://img2.meite.com/questions/202307/1364af578624075.png" />。（）  </p><p>答 案：错</p><p>解 析：<img src="https://img2.meite.com/questions/202212/06638ef8852e1bd.png" />所以<img src="https://img2.meite.com/questions/202212/06638ef88b66bc1.png" />  </p><p class="introTit">单选题</p><p>1、<img src="https://img2.meite.com/questions/202408/1966c2e4de7de2e.png" />（）。  </p><ul><li>A：<img src='https://img2.meite.com/questions/202408/1966c2e4e21e420.png' /></li><li>B：<img src='https://img2.meite.com/questions/202408/1966c2e4e5d0b4b.png' /></li><li>C：<img src='https://img2.meite.com/questions/202408/1966c2e4e949bd3.png' /></li><li>D：<img src='https://img2.meite.com/questions/202408/1966c2e4ed5b143.png' /></li></ul><p>答 案：C</p><p>解 析：<img src="https://img2.meite.com/questions/202408/1966c2e4f3033d6.png" /></p><p>2、定积分<img src="https://img2.meite.com/questions/202212/07639008d58dc33.png" />等于（）</p><ul><li>A：<img src='https://img2.meite.com/questions/202212/07639008e04ba1d.png' /></li><li>B：<img src='https://img2.meite.com/questions/202212/07639008ec023e8.png' /></li><li>C：<img src='https://img2.meite.com/questions/202212/07639008f77bcdf.png' /></li><li>D：<img src='https://img2.meite.com/questions/202212/076390090103b88.png' /></li></ul><p>答 案：A</p><p>解 析：<img src="https://img2.meite.com/questions/202212/07639009133aaa5.png" /><img src="https://img2.meite.com/questions/202212/07639009257f9f3.png" /></p><p class="introTit">主观题</p><p>1、求由方程siny＋xe^y＝0确定的曲线在点（0，π）处的切线方程．</p><p>答 案：解：方程两边对x求导得<img src="https://img2.meite.com/questions/202212/07638ff644b304e.png" />得<img src="https://img2.meite.com/questions/202212/07638ff6525e5d7.png" />所以<img src="https://img2.meite.com/questions/202212/07638ff660f27da.png" />,故所求切线方程为y－π＝e^π（x－0）,即e^πx－y＋π＝0</p><p>2、已知函数f(x)＝－x²＋2x．（1）求曲线y＝f(x)与x轴所围成的平面图形的面积S；<br />（2）求（1）中的平面图形绕x轴旋转一周所得旋转体的体积V．</p><p>答 案：解：（1）由<img src="https://img2.meite.com/questions/202212/05638d5a4828a6c.png" />得曲线与x轴交点坐标为（0，0），（2，0）．<img src="https://img2.meite.com/questions/202212/05638d5a5bab1e4.png" />（2）<img src="https://img2.meite.com/questions/202212/05638d5a6c4ad19.png" /></p><p class="introTit">填空题</p><p>1、<img src="https://img2.meite.com/questions/202212/06638ebc8706c7d.png" />（）．</p><p>答 案：<img src="https://img2.meite.com/questions/202212/06638ebc92aabc8.png" /></p><p>解 析：由等价无穷小知<img src="https://img2.meite.com/questions/202212/06638ebca2d68cd.png" />，<img src="https://img2.meite.com/questions/202212/06638ebcb529b96.png" />，所以<img src="https://img2.meite.com/questions/202212/06638ed6d4d4709.png" /></p><p>2、<img src="https://img2.meite.com/questions/202303/206417f999f22de.png" />（）</p><p>答 案：<img src="https://img2.meite.com/questions/202303/206417f9ace5537.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202303/206417f9bfa54f4.png" /><img src="https://img2.meite.com/questions/202303/206417f9c55298f.png" /></p><p class="introTit">简答题</p><p>1、<img src="https://img2.meite.com/questions/202408/1966c2ba62d9081.png" />  </p><p>答 案：<img src="https://img2.meite.com/questions/202408/1966c2ba66c879f.png" /></p><p>2、求函数<img src="https://img2.meite.com/questions/202204/2562660e19e39fc.png" />的单调区间、极值及函数曲线的凸凹性区间、拐点和渐近线.</p><p>答 案：<img src="https://img2.meite.com/questions/202204/256266103aab823.png" /><img src="https://img2.meite.com/questions/202204/2562661046e0549.png" />所以函数y的单调增区间为<img src="https://img2.meite.com/questions/202204/2562661067d7186.png" />单调减区间为（0,1）；函数y的凸区间为<img src="https://img2.meite.com/questions/202204/25626611135d877.png" />凹区间为<img src="https://img2.meite.com/questions/202204/256266112020f6d.png" />故x=0时，函数有极大值0，x=1时，函数有极小值-1，且点<img src="https://img2.meite.com/questions/202204/256266118962fa6.png" />为拐点，因<img src="https://img2.meite.com/questions/202204/2562661199f2f22.png" />不存在，且<img src="https://img2.meite.com/questions/202204/25626611a774dee.png" />没有无意义的点，故函数没有渐近线。</p>