2024年成考专升本《高等数学一》每日一练试题04月13日

<p class="introTit">单选题</p><p>1、微分方程<img src="https://img2.meite.com/questions/202211/17637600fbe28cd.png" />的通解为（）。</p><ul><li>A：<img src='https://img2.meite.com/questions/202211/176376010788b46.png' /></li><li>B：<img src='https://img2.meite.com/questions/202211/1763760112a06bb.png' /></li><li>C：<img src='https://img2.meite.com/questions/202211/176376011f85bd6.png' /></li><li>D：<img src='https://img2.meite.com/questions/202211/176376012aefd40.png' /></li></ul><p>答 案：C</p><p>解 析：所给方程为可分离变量方程，分离变量得<img src="https://img2.meite.com/questions/202211/176376013a3005e.png" />，等式两边分别积分得，<img src="https://img2.meite.com/questions/202211/176376014b92d0e.png" />，即<img src="https://img2.meite.com/questions/202211/1763760168d62cd.png" />。</p><p>2、<img src="https://img2.meite.com/questions/202211/296385bd68c1619.png" />（）。</p><ul><li>A：<img src='https://img2.meite.com/questions/202211/296385bd890a326.png' /></li><li>B：<img src='https://img2.meite.com/questions/202211/296385bd940a8a3.png' /></li><li>C：<img src='https://img2.meite.com/questions/202211/296385bdad706bd.png' /></li><li>D：<img src='https://img2.meite.com/questions/202211/296385bdc434e7d.png' /></li></ul><p>答 案：A</p><p>解 析：<img src="https://img2.meite.com/questions/202211/296385bdda62294.png" />，因此将x＝0代入得<img src="https://img2.meite.com/questions/202211/296385bdf27784f.png" />。</p><p>3、设z＝x^3y,则<img src="https://img2.meite.com/questions/202212/01638841c6daa34.png" />＝（）.</p><ul><li>A：<img src='https://img2.meite.com/questions/202212/01638841d11f555.png' /></li><li>B：<img src='https://img2.meite.com/questions/202212/01638841db06fde.png' /></li><li>C：<img src='https://img2.meite.com/questions/202212/01638841e614a34.png' /></li><li>D：<img src='https://img2.meite.com/questions/202212/01638841f115e39.png' /></li></ul><p>答 案：D</p><p>解 析：将x看为常数，因此z为y的指数函数，可知<img src="https://img2.meite.com/questions/202212/01638842059f002.png" />。</p><p class="introTit">主观题</p><p>1、设f(x)是以T为周期的连续函数，a为任意常数，证明：<img src="https://img2.meite.com/questions/202212/01638810a04c178.png" />。</p><p>答 案：证：因为<img src="https://img2.meite.com/questions/202212/01638810b105867.png" />令x＝T＋t，做变量替换得<img src="https://img2.meite.com/questions/202212/01638810cade25f.png" />故<img src="https://img2.meite.com/questions/202212/01638810de0e205.png" /></p><p>2、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>3、设函数<img src="https://img2.meite.com/questions/202211/176375da8476d02.png" />在x＝0处连续，求常数a的值</p><p>答 案：解：f（x）在x＝0处连续，则<img src="https://img2.meite.com/questions/202211/176375daa0c1850.png" />，<img src="https://img2.meite.com/questions/202211/176375daca19cb0.png" />故<img src="https://img2.meite.com/questions/202211/176375dadef0631.png" />。</p><p class="introTit">填空题</p><p>1、<img src="https://img2.meite.com/questions/202211/176375a1737fdb5.png" />（）。</p><p>答 案：e⁴</p><p>解 析：<img src="https://img2.meite.com/questions/202211/176375a18457b79.png" /></p><p>2、设<img src="https://img2.meite.com/questions/202211/1663749668dfd94.png" />，则dy＝（）。</p><p>答 案：<img src="https://img2.meite.com/questions/202211/166374967ad0538.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202211/1663749691999a6.png" /></p><p>3、<img src="https://img2.meite.com/questions/202211/186376e17e3e3db.png" />＝（）。</p><p>答 案：x-x²+C</p><p>解 析：<img src="https://img2.meite.com/questions/202211/186376e19ea093b.png" /></p><p class="introTit">简答题</p><p>1、设f(x)=<img src="https://img2.meite.com/questions/202303/1764140cba28156.png" />在x=0连续，试确定A,B.</p><p>答 案：<img src="https://img2.meite.com/questions/202303/1764140ce7d0fb9.png" /> <img src="https://img2.meite.com/questions/202303/1764140cf387f0c.png" /> 欲使f(x)在x=0处连续，应有2A=4=B+1，所以A=2,B=3.  </p>