2024年成考专升本《高等数学一》每日一练试题07月01日

<p class="introTit">单选题</p><p>1、<img src="https://img2.meite.com/question/import/cb1a6986c0a3a727106cf5fb7deadd60.png" /></p><ul><li>A：6Y</li><li>B：6XY</li><li>C：3X</li><li>D：3X²</li></ul><p>答 案：D</p><p>2、函数f(x)=<img src="https://img2.meite.com/questions/202303/17641415a1ccfaf.png" />在x=0处（）</p><ul><li>A：连续且可导</li><li>B：连续且不可导</li><li>C：不连续</li><li>D：不仅可导,导数也连续</li></ul><p>答 案：B</p><p>解 析：因为<img src="https://img2.meite.com/questions/202303/17641415dd9e8de.png" />所以函数在x=0处连续，又因<img src="https://img2.meite.com/questions/202303/176414160d3fe80.png" /><img src="https://img2.meite.com/questions/202303/17641416228c345.png" />不存在，所以函数在x=0处不可导。</p><p>3、<img src="https://img2.meite.com/questions/202211/2863847cb50e4ef.png" />＝（）。</p><ul><li>A：<img src='https://img2.meite.com/questions/202211/2863847cbf98ec8.png' /></li><li>B：-<img src='https://img2.meite.com/questions/202211/2863847cc0a9a5f.png' /></li><li>C：±<img src='https://img2.meite.com/questions/202211/2863847cc4e816c.png' /></li><li>D：不存在</li></ul><p>答 案：D</p><p>解 析：<img src="https://img2.meite.com/questions/202211/2863847cd251b10.png" />，<img src="https://img2.meite.com/questions/202211/2863847cdf86060.png" />，所以<img src="https://img2.meite.com/questions/202211/2863847cef6ee2d.png" />不存在。</p><p class="introTit">主观题</p><p>1、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>2、求微分方程<img src="https://img2.meite.com/questions/202212/03638ac06ec86af.png" />满足初始条件<img src="https://img2.meite.com/questions/202212/03638ac07e02535.png" />的特解。</p><p>答 案：解：将方程改写为<img src="https://img2.meite.com/questions/202212/03638ac08d6874b.png" />，<img src="https://img2.meite.com/questions/202212/03638ac09c022b3.png" />，则<img src="https://img2.meite.com/questions/202212/03638ac0d3cb0a3.png" />故方程通解为<img src="https://img2.meite.com/questions/202212/03638ac103b9bff.png" />将<img src="https://img2.meite.com/questions/202212/03638ac115367e7.png" />代入通解，得<img src="https://img2.meite.com/questions/202212/03638ac1227c548.png" />从而所求满足初始条件<img src="https://img2.meite.com/questions/202212/03638ac131946df.png" />的特解为<img src="https://img2.meite.com/questions/202212/03638ac14122147.png" /></p><p>3、计算<img src="https://img2.meite.com/questions/202212/0163880f1f1db81.png" /></p><p>答 案：解：令<img src="https://img2.meite.com/questions/202212/0163880f2c78d6e.png" />当x＝4时，t＝2；当x＝9时，t＝3。则有<img src="https://img2.meite.com/questions/202212/0163880f445e340.png" /><img src="https://img2.meite.com/questions/202212/0163880f6263be5.png" /></p><p class="introTit">填空题</p><p>1、<img src="https://img2.meite.com/questions/202211/176375d4a6846cc.png" />（）。</p><p>答 案：e^-3</p><p>解 析：所给极限为重要极限的形式，由<img src="https://img2.meite.com/questions/202211/176375d4be3d81b.png" />，可得<img src="https://img2.meite.com/questions/202211/176375d4ca53ef0.png" /></p><p>2、设y＝(x＋3)²，则y'＝（）。</p><p>答 案：2(x＋3)</p><p>解 析：<img src="https://img2.meite.com/questions/202211/166374579ad741f.png" /></p><p>3、<img src="https://img2.meite.com/questions/202211/166374969fb8701.png" />＝（）。</p><p>答 案：5sinx＋C</p><p>解 析：<img src="https://img2.meite.com/questions/202211/166374976f80278.png" /></p><p class="introTit">简答题</p><p>1、设D是由曲线<img src="https://img2.meite.com/questions/202405/166645be83cfdf4.png" />，x=0，y=0所围成的平面图形. (1)求D的面积S； (2)求D绕x轴旋转一周所得旋转体的体积V.  </p><p>答 案：<img src="https://img2.meite.com/questions/202405/166645be8b845c8.png" /></p>