2024年成考专升本《高等数学一》每日一练试题09月14日

<p class="introTit">单选题</p><p>1、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>2、设函数f(x)在x＝x₀处可导，且<img src="https://img2.meite.com/questions/202211/296385c62f5c4f1.png" />＝2，则<img src="https://img2.meite.com/questions/202211/296385c63e9dae7.png" />等于（）。</p><ul><li>A：<img src='https://img2.meite.com/questions/202211/296385c6494f82f.png' /></li><li>B：2</li><li>C：0</li><li>D：4</li></ul><p>答 案：D</p><p>解 析：依题意得<img src="https://img2.meite.com/questions/202211/296385c6587ac0c.png" /><img src="https://img2.meite.com/questions/202211/296385c666d2239.png" /></p><p>3、微分方程<img src="https://img2.meite.com/questions/202408/1666bebc5c1bd71.png" />的通解为（）。  </p><ul><li>A：<img src='https://img2.meite.com/questions/202408/1666bebc60d8f7f.png' /></li><li>B：<img src='https://img2.meite.com/questions/202408/1666bebc64c7ef4.png' /></li><li>C：<img src='https://img2.meite.com/questions/202408/1666bebc6954292.png' /></li><li>D：<img src='https://img2.meite.com/questions/202408/1666bebc6d4dfd0.png' /></li></ul><p>答 案：C</p><p>解 析：<img src="https://img2.meite.com/questions/202408/1666bebc72332d5.png" /></p><p class="introTit">主观题</p><p>1、求<img src="https://img2.meite.com/questions/202211/2963856b9fa7d50.png" /></p><p>答 案：解：<img src="https://img2.meite.com/questions/202211/2963856bb1eca82.png" /><img src="https://img2.meite.com/questions/202211/2963856bc769de2.png" /></p><p>2、求<img src="https://img2.meite.com/questions/202211/2963856d739281b.png" /></p><p>答 案：解：<img src="https://img2.meite.com/questions/202211/2963856d85b32dd.png" /><img src="https://img2.meite.com/questions/202211/2963856d978d53a.png" />。</p><p>3、求微分方程y'－<img src="https://img2.meite.com/questions/202212/03638ac17eaa5ba.png" />＝lnx满足初始条件<img src="https://img2.meite.com/questions/202212/03638ac1908c65f.png" />＝1的特解。</p><p>答 案：解：P（x）＝<img src="https://img2.meite.com/questions/202212/03638ac1a3efa02.png" />，Q（x）＝lnx，则<img src="https://img2.meite.com/questions/202212/03638ac1b4c4f05.png" />所以<img src="https://img2.meite.com/questions/202212/03638ac1c719a0f.png" />将<img src="https://img2.meite.com/questions/202212/03638ac1d4d883b.png" />＝1代入y式，得C＝1．故所求特解为<img src="https://img2.meite.com/questions/202212/03638ac2042e0a4.png" />。</p><p class="introTit">填空题</p><p>1、设y=f（x）在点x=0处可导，且x=0为f（x）的极值点，则f’（0）=（）。  </p><p>答 案：0</p><p>解 析：本题考查的知识点为极值的必要条件。 <img src="https://img2.meite.com/questions/202408/1566bdc121a0e09.png" />  </p><p>2、<img src="https://img2.meite.com/questions/202408/1666bef98c84462.png" />  </p><p>答 案：<img src="https://img2.meite.com/questions/202408/1666bef990dd710.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202408/1666bef995b9ddf.png" /></p><p>3、<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 class="introTit">简答题</p><p>1、<img src="https://img2.meite.com/questions/202303/17641426bb3e6fd.png" /></p><p>答 案：<img src="https://img2.meite.com/questions/202303/17641426cdbf5a7.png" /></p>