2025年成考专升本《高等数学一》每日一练试题01月30日

<p class="introTit">单选题</p><p>1、已知<img src="https://img2.meite.com/questions/202211/3063871e8c3c821.png" />，则<img src="https://img2.meite.com/questions/202211/3063871ea1389f4.png" />（）。</p><ul><li>A：－cosx＋C</li><li>B：cosx＋C</li><li>C：<img src='https://img2.meite.com/questions/202211/3063871eb2afdac.png' /></li><li>D：<img src='https://img2.meite.com/questions/202211/3063871ebc4801d.png' /></li></ul><p>答 案：C</p><p>解 析：已知<img src="https://img2.meite.com/questions/202211/3063871ecc7110c.png" />，在此式两侧对cosx求积分，得<img src="https://img2.meite.com/questions/202211/3063871eded0d64.png" />有<img src="https://img2.meite.com/questions/202211/3063871ef7dbe12.png" /></p><p>2、下列命题中正确的有（）。  </p><ul><li>A：<img src='https://img2.meite.com/questions/202408/1666beee5dbb517.png' /></li><li>B：<img src='https://img2.meite.com/questions/202408/1666beee61969bf.png' /></li><li>C：<img src='https://img2.meite.com/questions/202408/1666beee6512209.png' /></li><li>D：<img src='https://img2.meite.com/questions/202408/1666beee686db8d.png' /></li></ul><p>答 案：B</p><p>解 析：<img src="https://img2.meite.com/questions/202408/1666beee6dec07d.png" /> <img src="https://img2.meite.com/questions/202408/1666beee7183d66.png" />  </p><p>3、级数<img src="https://img2.meite.com/questions/202212/0163885515b244e.png" />（k为非零常数）（）。</p><ul><li>A：发散</li><li>B：绝对收敛</li><li>C：条件收敛</li><li>D：收敛性与k有关</li></ul><p>答 案：C</p><p>解 析：级数各项取绝对值得级数<img src="https://img2.meite.com/questions/202212/016388552b2e6d2.png" />为发散级数；由莱布尼茨判别法可知<img src="https://img2.meite.com/questions/202212/016388553fc0466.png" />收敛，故<img src="https://img2.meite.com/questions/202212/0163885551ad5f1.png" />为条件收敛。</p><p class="introTit">主观题</p><p>1、设z＝xy²＋e^ycosx，求<img src="https://img2.meite.com/questions/202211/16637481f262f04.png" />．</p><p>答 案：解：z＝xy²＋e^ycosx，<img src="https://img2.meite.com/questions/202211/1663748277d6f76.png" />＝2xy＋e^ycosx。</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、<img src="https://img2.meite.com/question/import/38122ef5ca6e8921ffc7a5a4cc1b3783.png" /></p><p>答 案：<img src="https://img2.meite.com/question/import/5dba69a2724d60821a1a3610ad6ceb11.png" /></p><p class="introTit">填空题</p><p>1、曲线f(x)＝x³－x上点（1，0）处的切线方程为（）。</p><p>答 案：y＝2x－2</p><p>解 析：<img src="https://img2.meite.com/questions/202211/306386b708c68ff.png" />，f'(1)＝2，故曲线在点（1，0）处的切线方程为y-0=2(x-1)，即y＝2x－2。</p><p>2、<img src="https://img2.meite.com/questions/202408/1666bf05e527c81.png" />  </p><p>答 案：<img src="https://img2.meite.com/questions/202408/1666bf05e91163b.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202408/1666bf05ece4a1d.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、<img src="https://img2.meite.com/questions/202408/1666befa05ba1da.png" />  </p><p>答 案：<img src="https://img2.meite.com/questions/202408/1666befa0a31852.png" /></p>