2024年成考专升本《高等数学一》每日一练试题04月07日

<p class="introTit">单选题</p><p>1、级数<img src="https://img2.meite.com/questions/202303/0364019dcba4672.png" />的收敛半径为（）</p><ul><li>A：<img src='https://img2.meite.com/questions/202303/0364019dee2b35c.png' /></li><li>B：1</li><li>C：<img src='https://img2.meite.com/questions/202303/0364019df7861a9.png' /></li><li>D：2</li></ul><p>答 案：B</p><p>解 析：由题可知<img src="https://img2.meite.com/questions/202303/036401ac6ceeef1.png" />因此级数的收敛半径为<img src="https://img2.meite.com/questions/202303/036401ac8805bbb.png" /></p><p>2、函数<img src="https://img2.meite.com/questions/202211/2863848501caa9e.png" />的连续区间是（）。</p><ul><li>A：（∞，2）<img src='https://img2.meite.com/questions/202211/28638484ebb9d5c.png' />（2，1）<img src='https://img2.meite.com/questions/202211/28638484ed1f185.png' />（1，＋∞）</li><li>B：[3，＋∞）</li><li>C：（∞，2）<img src='https://img2.meite.com/questions/202211/28638485094fc55.png' />（2，＋∞）</li><li>D：（∞，1）<img src='https://img2.meite.com/questions/202211/286384850a28820.png' />（1，＋∞）</li></ul><p>答 案：B</p><p>解 析：函数在定义域内是连续的，故<img src="https://img2.meite.com/questions/202211/28638485202a043.png" />，得<img src="https://img2.meite.com/questions/202211/286384852bd4d86.png" />.故函数的连续区间为[3，＋∞）。</p><p>3、<img src="https://img2.meite.com/questions/202211/296385bd68c1619.png" />（）。</p><ul><li>A：<img src='https://img2.meite.com/questions/202211/296385bd890a326.png' /></li><li>B：<img src='https://img2.meite.com/questions/202211/296385bd940a8a3.png' /></li><li>C：<img src='https://img2.meite.com/questions/202211/296385bdad706bd.png' /></li><li>D：<img src='https://img2.meite.com/questions/202211/296385bdc434e7d.png' /></li></ul><p>答 案：A</p><p>解 析：<img src="https://img2.meite.com/questions/202211/296385bdda62294.png" />，因此将x＝0代入得<img src="https://img2.meite.com/questions/202211/296385bdf27784f.png" />。</p><p class="introTit">主观题</p><p>1、设f(x)为连续函数，且满足方程<img src="https://img2.meite.com/questions/202212/01638810f7bffb5.png" />求<img src="https://img2.meite.com/questions/202212/0163881108e6c07.png" />的值。</p><p>答 案：解：<img src="https://img2.meite.com/questions/202212/016388111956428.png" />等式两边分别积分可得<img src="https://img2.meite.com/questions/202212/01638811340181e.png" />故<img src="https://img2.meite.com/questions/202212/0163881146dd7a0.png" />，即<img src="https://img2.meite.com/questions/202212/0163881158d081c.png" />。</p><p>2、求曲线y＝sinx、y＝cosx、直线x＝0在第一象限所围图形的面积A及该图形绕x轴旋转一周所得旋转体的体积V_x。</p><p>答 案：解：由<img src="https://img2.meite.com/questions/202212/01638816eb363c4.png" />，解得两曲线交点的x坐标为<img src="https://img2.meite.com/questions/202212/01638816fe2c575.png" />。<img src="https://img2.meite.com/questions/202212/016388176a0f817.png" /><img src="https://img2.meite.com/questions/202212/016388174e5df94.png" /><img src="https://img2.meite.com/questions/202212/0163881729a711e.png" /><img src="https://img2.meite.com/questions/202212/016388173bbef42.png" /></p><p>3、设<img src="https://img2.meite.com/questions/202211/166374ab053a051.png" />，求y'．</p><p>答 案：解：<img src="https://img2.meite.com/questions/202211/166374acf55bc71.png" /></p><p class="introTit">填空题</p><p>1、设I=<img src="https://img2.meite.com/questions/202303/176414030ee674e.png" />交换积分次序，则有I=（）</p><p>答 案：<img src="https://img2.meite.com/questions/202303/176414032f6347a.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202303/1764140336b7f20.png" />的积分区域<img src="https://img2.meite.com/questions/202303/176414034e05ef7.png" /><img src="https://img2.meite.com/questions/202303/17641403566791e.png" /><img src="https://img2.meite.com/questions/202303/176414035c360c7.png" /></p><p>2、<img src="https://img2.meite.com/questions/202212/01638805d88ecb5.png" />则<img src="https://img2.meite.com/questions/202212/01638805ea0961f.png" />（）。</p><p>答 案：3</p><p>解 析：<img src="https://img2.meite.com/questions/202212/01638805fb1e3c1.png" /></p><p>3、设<img src="https://img2.meite.com/questions/202211/306387248fa2011.png" />，则f'(x)＝（）。</p><p>答 案：2xsinx²-sinx</p><p>解 析：<img src="https://img2.meite.com/questions/202211/30638724baf2b96.png" />。</p><p class="introTit">简答题</p><p>1、求<img src="https://img2.meite.com/questions/202303/036401a0a3e00d2.png" />  </p><p>答 案：<img src="https://img2.meite.com/questions/202303/036401afab6aba9.png" /></p>