2024年成考专升本《高等数学一》每日一练试题06月12日

<p class="introTit">单选题</p><p>1、设区域<img src="https://img2.meite.com/questions/202212/01638844dd39531.png" />，则<img src="https://img2.meite.com/questions/202212/01638844ea2b747.png" />＝（）。</p><ul><li>A：<img src='https://img2.meite.com/questions/202212/01638844f643e91.png' /></li><li>B：1</li><li>C：<img src='https://img2.meite.com/questions/202212/01638845004a817.png' /></li><li>D：<img src='https://img2.meite.com/questions/202212/01638845095373c.png' /></li></ul><p>答 案：C</p><p>解 析：<img src="https://img2.meite.com/questions/202212/016388451586059.png" />。</p><p>2、若级数<img src="https://img2.meite.com/questions/202212/01638854cfa0e9b.png" />收敛，则<img src="https://img2.meite.com/questions/202212/01638854db021ec.png" />（）。</p><ul><li>A：发散</li><li>B：条件收敛</li><li>C：绝对收敛</li><li>D：无法判定敛散性</li></ul><p>答 案：C</p><p>解 析：级数绝对收敛的性质可知，<img src="https://img2.meite.com/questions/202212/01638854ef9f908.png" />收敛，则<img src="https://img2.meite.com/questions/202212/01638855016b01e.png" />收敛，且为绝对收敛。</p><p>3、微分方程<img src="https://img2.meite.com/questions/202211/16637454177b20a.png" />的阶数为（）。</p><ul><li>A：1</li><li>B：2</li><li>C：3</li><li>D：4</li></ul><p>答 案：A</p><p>解 析：微分方程<img src="https://img2.meite.com/questions/202211/166374541f0f375.png" />所含有未知函数y的导数最高阶数为1，为一阶微分方程。</p><p class="introTit">主观题</p><p>1、设<img src="https://img2.meite.com/questions/202211/176375db1bc430b.png" />，求<img src="https://img2.meite.com/questions/202211/176375db347e4aa.png" /></p><p>答 案：解：由题意得<img src="https://img2.meite.com/questions/202211/176375db4b0058a.png" />故<img src="https://img2.meite.com/questions/202211/176375db5f00621.png" />。</p><p>2、求<img src="https://img2.meite.com/questions/202211/2963856ce27e6d8.png" /></p><p>答 案：解：<img src="https://img2.meite.com/questions/202211/2963856cf281662.png" /><img src="https://img2.meite.com/questions/202211/2963856d0bd9b82.png" /></p><p>3、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 class="introTit">填空题</p><p>1、<img src="https://img2.meite.com/questions/202211/166374960774219.png" />（）。</p><p>答 案：</p><p>解 析：<img src="https://img2.meite.com/questions/202211/166374961c0a5be.png" /></p><p>2、设z＝x^y，则<img src="https://img2.meite.com/questions/202212/0163884840e11ad.png" />（）。</p><p>答 案：<img src="https://img2.meite.com/questions/202212/016388484db0d71.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202212/016388485a8b000.png" />，求<img src="https://img2.meite.com/questions/202212/0163884840e11ad.png" />时，将y认作常量，z为x的幂函数，<img src="https://img2.meite.com/questions/202212/01638848719e1e1.png" />。</p><p>3、设<img src="https://img2.meite.com/questions/202212/03638aeab160574.png" />，<img src="https://img2.meite.com/questions/202212/03638aeac2016a6.png" />，则g'(x)＝（）。</p><p>答 案：<img src="https://img2.meite.com/questions/202212/03638aead6c9cb7.png" /></p><p>解 析：令t＝x＋1则x＝t－1，<img src="https://img2.meite.com/questions/202212/03638aeae9a9348.png" />，则<img src="https://img2.meite.com/questions/202212/03638aeaf6c8618.png" />,<img src="https://img2.meite.com/questions/202212/03638aeb0738a24.png" />。</p><p class="introTit">简答题</p><p>1、<img src="https://img2.meite.com/questions/202303/1764140b5eb19d9.png" /></p><p>答 案：<img src="https://img2.meite.com/questions/202303/1764140b998c053.png" /></p>