2024年成考专升本《高等数学一》每日一练试题04月21日

<p class="introTit">单选题</p><p>1、在空间直角坐标系中，方程x²＋z²＝z的图形是（）。</p><ul><li>A：圆柱面</li><li>B：圆</li><li>C：抛物线</li><li>D：旋转抛物面</li></ul><p>答 案：A</p><p>解 析：方程x²＋z²＝z可变形为<img src="https://img2.meite.com/questions/202212/0163881bbd64d42.png" />，由此知该方程表示的是准线为圆、母线平行于y轴的圆柱面。</p><p>2、设<img src="https://img2.meite.com/questions/202211/296385bf727e466.png" />，则<img src="https://img2.meite.com/questions/202211/296385bf807cf47.png" />（）。</p><ul><li>A：2</li><li>B：<img src='https://img2.meite.com/questions/202211/296385bf8b266c9.png' /></li><li>C：－2</li><li>D：<img src='https://img2.meite.com/questions/202211/296385bf95c28e7.png' /></li></ul><p>答 案：B</p><p>解 析：<img src="https://img2.meite.com/questions/202211/296385bfa4dbd46.png" />,<img src="https://img2.meite.com/questions/202211/296385bfb44139f.png" />。</p><p>3、矩阵<img src="https://img2.meite.com/questions/202202/126207786eb8557.png" />的秩是（）</p><ul><li>A：0</li><li>B：1</li><li>C：2</li><li>D：3</li></ul><p>答 案：C</p><p>解 析：<img src="https://img2.meite.com/questions/202202/12620778bb57938.png" /> <img src="https://img2.meite.com/questions/202202/12620778c5bee8e.png" /></p><p class="introTit">主观题</p><p>1、求极限<img src="https://img2.meite.com/questions/202211/296385748b0aa2e.png" />。</p><p>答 案：解：<img src="https://img2.meite.com/questions/202211/296385749dcae40.png" /></p><p>2、求<img src="https://img2.meite.com/questions/202212/0163880ec16943e.png" />。</p><p>答 案：解：<img src="https://img2.meite.com/questions/202212/0163880ed358bb0.png" /></p><p>3、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 class="introTit">填空题</p><p>1、已知f（x）的一个原函数为<img src="https://img2.meite.com/questions/202212/03638afcec77a43.png" />，则<img src="https://img2.meite.com/questions/202212/03638afcf9213ea.png" />＝（）。</p><p>答 案：<img src="https://img2.meite.com/questions/202212/03638afd04dc1fb.png" /></p><p>解 析：因为f（x）的一个原函数为<img src="https://img2.meite.com/questions/202212/03638afd13bd32b.png" />，则<img src="https://img2.meite.com/questions/202212/03638afd1ba529c.png" />所以有<img src="https://img2.meite.com/questions/202212/03638afd30df818.png" />。</p><p>2、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>3、<img src="https://img2.meite.com/questions/202211/166374977dc9993.png" />＝（）。</p><p>答 案：ln2</p><p>解 析：<img src="https://img2.meite.com/questions/202211/166374978c5ad27.png" /></p><p class="introTit">简答题</p><p>1、设函数z(x,y)由方程<img src="https://img2.meite.com/questions/202303/176414074ee99be.png" />所确定 证明：<img src="https://img2.meite.com/questions/202303/176414075c587da.png" /></p><p>答 案：<img src="https://img2.meite.com/questions/202303/176414076fa1487.png" /> <img src="https://img2.meite.com/questions/202303/176414077960454.png" />所以<img src="https://img2.meite.com/questions/202303/176414077fe7935.png" /><img src="https://img2.meite.com/questions/202303/17641407920ce9d.png" />  </p>