2024年成考专升本《高等数学一》每日一练试题11月11日

<p class="introTit">单选题</p><p>1、设<img src="https://img2.meite.com/questions/202211/176375facc9c77f.png" />（）。</p><ul><li>A：2x－2e</li><li>B：<img src='https://img2.meite.com/questions/202211/176375faddef1a8.png' /></li><li>C：2x－e</li><li>D：2x</li></ul><p>答 案：D</p><p>解 析：<img src="https://img2.meite.com/questions/202211/176375faff47c30.png" />则<img src="https://img2.meite.com/questions/202211/176375fb11d891b.png" />。</p><p>2、设函数f(x)满足<img src="https://img2.meite.com/questions/202303/176413e0e837e78.png" />且f(0)=0,则f(x)=()</p><ul><li>A：<img src='https://img2.meite.com/questions/202303/176413e11e492e3.png' /></li><li>B：<img src='https://img2.meite.com/questions/202303/176413e113de62f.png' /></li><li>C：<img src='https://img2.meite.com/questions/202303/176413e1196224a.png' /></li><li>D：<img src='https://img2.meite.com/questions/202303/176413e10cadab6.png' /></li></ul><p>答 案：D</p><p>解 析：由<img src="https://img2.meite.com/questions/202303/176413e0e837e78.png" />知<img src="https://img2.meite.com/questions/202303/176413e16f36bbb.png" />令<img src="https://img2.meite.com/questions/202303/176413e17d276a1.png" />故<img src="https://img2.meite.com/questions/202303/176413e184a50ac.png" />所以f(u)=u-<img src="https://img2.meite.com/questions/202303/176413e1ab07ac9.png" />由f(0)=0，得C=0.所以<img src="https://img2.meite.com/questions/202303/176413e1c444863.png" /></p><p>3、级数<img src="https://img2.meite.com/questions/202212/016388557833724.png" />（a为大于零的常数）（）。</p><ul><li>A：绝对收敛</li><li>B：条件收敛</li><li>C：发散</li><li>D：收敛性与a有关</li></ul><p>答 案：A</p><p>解 析：<img src="https://img2.meite.com/questions/202212/01638855b02a9c3.png" /><img src="https://img2.meite.com/questions/202212/01638855c11e7de.png" />级数，因此为收敛级数，由级数性质可知<img src="https://img2.meite.com/questions/202212/01638855d964fc3.png" />绝对收敛。</p><p class="introTit">主观题</p><p>1、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>2、计算<img src="https://img2.meite.com/questions/202212/0163881002028f4.png" />。</p><p>答 案：解：令<img src="https://img2.meite.com/questions/202212/016388100f15b4f.png" />，<img src="https://img2.meite.com/questions/202212/016388101acc2b6.png" />，则<img src="https://img2.meite.com/questions/202212/016388102e413ca.png" /></p><p>3、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 class="introTit">填空题</p><p>1、若<img src="https://img2.meite.com/questions/202212/01638804afa9183.png" />，且f（0）＝1，则f(x)＝（）。</p><p>答 案：<img src="https://img2.meite.com/questions/202212/01638804c5c4df8.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202212/01638804d3efec5.png" />＝1＋e^2x，等式两边对e^x积分有<img src="https://img2.meite.com/questions/202212/01638804efcda29.png" /><img src="https://img2.meite.com/questions/202212/01638805008b68c.png" />所以<img src="https://img2.meite.com/questions/202212/01638805145ae2a.png" /></p><p>2、设z＝x²-y，则dz＝（）。</p><p>答 案：2xdx－dy</p><p>解 析：<img src="https://img2.meite.com/questions/202211/1663749ad5afb18.png" /></p><p>3、过点(1,0,-1)与平面3x-y-z-2=0平行的平面的方程为（）</p><p>答 案：3x-y-z-4=0</p><p>解 析：平面3x-y-z-2=0的法向量为(3，-1，-1)，所求平面与其平行，故所求的平面的法向量为(3，-1，-1)，由平面的点法式方程得所求平面方程为3(x-1)-(y-0)-(z+1)=0，及3x-y-z-4=0。</p><p class="introTit">简答题</p><p>1、计算<img src="https://img2.meite.com/questions/202405/166645be9260e6a.png" />，其中D是由曲线<img src="https://img2.meite.com/questions/202405/166645be9786e84.png" />，y＝x，y＝-x所围成的闭区域.  </p><p>答 案：积分区域用极坐标可表示为<img src="https://img2.meite.com/questions/202405/166645be9db576b.png" /> 故<img src="https://img2.meite.com/questions/202405/166645bea4182fa.png" />  </p>