2025年成考专升本《高等数学一》每日一练试题05月08日

<p class="introTit">单选题</p><p>1、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>2、<img src="https://img2.meite.com/questions/202408/1666bec688e0f0f.png" />（）。  </p><ul><li>A：<img src='https://img2.meite.com/questions/202408/1666bec68dcc527.png' /></li><li>B：<img src='https://img2.meite.com/questions/202408/1666bec691ad4e4.png' /></li><li>C：<img src='https://img2.meite.com/questions/202408/1666bec696a886c.png' /></li><li>D：<img src='https://img2.meite.com/questions/202408/1666bec69ac5980.png' /></li></ul><p>答 案：A</p><p>解 析：<img src="https://img2.meite.com/questions/202408/1666bec69fb6916.png" /><img src="https://img2.meite.com/questions/202408/1666bec6a47ea79.png" /></p><p>3、<img src="https://img2.meite.com/questions/202408/1666bebbcdc48e6.png" />（）。  </p><ul><li>A：1/2</li><li>B：1</li><li>C：<img src='https://img2.meite.com/questions/202408/1666bebbd270492.png' /></li><li>D：<img src='https://img2.meite.com/questions/202408/1666bebbd6af098.png' /></li></ul><p>答 案：B</p><p>解 析：<img src="https://img2.meite.com/questions/202408/1666bebbdb445e7.png" /></p><p class="introTit">主观题</p><p>1、设<img src="https://img2.meite.com/questions/202211/186376eced1a5f9.png" />求dz。</p><p>答 案：解：<img src="https://img2.meite.com/questions/202211/186376ed05f22a7.png" /><img src="https://img2.meite.com/questions/202211/186376ed16f1c28.png" /></p><p>2、求微分方程<img src="https://img2.meite.com/questions/202212/03638ac38e5fd44.png" />的通解。</p><p>答 案：解：对应的齐次方程为<img src="https://img2.meite.com/questions/202212/03638ac39bb126c.png" />。特征方程<img src="https://img2.meite.com/questions/202212/03638ac3abef614.png" />，特征根<img src="https://img2.meite.com/questions/202212/03638ac3bb18486.png" />齐次方程通解为<img src="https://img2.meite.com/questions/202212/03638ac3c81e1f0.png" />原方程特解为<img src="https://img2.meite.com/questions/202212/03638ac3d7442b3.png" />，代入原方程可得<img src="https://img2.meite.com/questions/202212/03638ac3ea0899f.png" />，因此<img src="https://img2.meite.com/questions/202212/03638ac3fe7cb5d.png" />。<br />方程通解为<img src="https://img2.meite.com/questions/202212/03638ac40c27e0d.png" /></p><p>3、求<img src="https://img2.meite.com/questions/202211/166374aae6ed5e7.png" /></p><p>答 案：解：利用洛必达法则，得<img src="https://img2.meite.com/questions/202211/166374aaf5e35bf.png" /></p><p class="introTit">填空题</p><p>1、<img src="https://img2.meite.com/questions/202303/1764141bea38c4f.png" />（）</p><p>答 案：<img src="https://img2.meite.com/questions/202303/1764141c03d308e.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202303/1764141c185c3e5.png" /><img src="https://img2.meite.com/questions/202303/1764141c1fe101b.png" /></p><p>2、微分方程y''＝x的通解是（）。</p><p>答 案：<img src="https://img2.meite.com/questions/202212/0163886f82df537.png" /></p><p>解 析：等式两边同时积分得<img src="https://img2.meite.com/questions/202212/0163886f95c7a8f.png" />，重复上一步骤得<img src="https://img2.meite.com/questions/202212/0163886fa4e4f0b.png" /></p><p>3、<img src="https://img2.meite.com/questions/202211/30638722026e1bf.png" />（）。</p><p>答 案：<img src="https://img2.meite.com/questions/202211/306387220ce46d3.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202211/306387221aad9d8.png" /></p><p class="introTit">简答题</p><p>1、计算<img src="https://img2.meite.com/questions/202405/166645c48ae9784.png" />  </p><p>答 案：<img src="https://img2.meite.com/questions/202405/166645c49761600.png" /></p>