2025年成考专升本《高等数学二》每日一练试题01月07日

<p class="introTit">判断题</p><p>1、若<img src="https://img2.meite.com/questions/202307/1364af5780970e6.png" />，则<img src="https://img2.meite.com/questions/202307/1364af578624075.png" />。（）  </p><p>答 案：错</p><p>解 析：<img src="https://img2.meite.com/questions/202212/06638ef8852e1bd.png" />所以<img src="https://img2.meite.com/questions/202212/06638ef88b66bc1.png" />  </p><p class="introTit">单选题</p><p>1、<img src="https://img2.meite.com/questions/202408/2066c4083ba15c0.png" />（）。  </p><ul><li>A：（1，1）</li><li>B：（e，e）</li><li>C：（1，e＋1）</li><li>D：（e，e＋2）</li></ul><p>答 案：A</p><p>解 析：本题将四个选项代入等式，只有选项A的坐标使等式成立。 <img src="https://img2.meite.com/questions/202408/2066c408408cf48.png" />  </p><p>2、设f(x)=arctanx，则<img src="https://img2.meite.com/questions/202212/06638ee1a8127ba.png" />=()</p><ul><li>A：<img src='https://img2.meite.com/questions/202212/06638ee1b657fc8.png' /></li><li>B：<img src='https://img2.meite.com/questions/202212/06638ee1bca2a58.png' /></li><li>C：<img src='https://img2.meite.com/questions/202212/06638ee1c1e5ce0.png' /></li><li>D：1</li></ul><p>答 案：B</p><p>解 析：函数f(x)在点x₀的导数定义为<img src="https://img2.meite.com/questions/202212/06638ee1f0de4e6.png" />，因为<img src="https://img2.meite.com/questions/202212/06638ee20222110.png" /> 所以<img src="https://img2.meite.com/questions/202212/06638ee20d1346d.png" />。</p><p class="introTit">主观题</p><p>1、计算<img src="https://img2.meite.com/questions/202212/06638e9ae957f4e.png" /></p><p>答 案：解：由洛必达法则得<img src="https://img2.meite.com/questions/202212/06638e9af6dd03c.png" /></p><p>2、设<img src="https://img2.meite.com/questions/202212/0863914f0f2ceb9.png" />，求证：<img src="https://img2.meite.com/questions/202212/0863914f19132dd.png" /></p><p>答 案：证：<img src="https://img2.meite.com/questions/202212/0863914f923f8f5.png" /><img src="https://img2.meite.com/questions/202212/0863914faa9fddd.png" /><img src="https://img2.meite.com/questions/202212/0863914fc694081.png" />，故<img src="https://img2.meite.com/questions/202212/0863914fd45de72.png" />．</p><p class="introTit">填空题</p><p>1、<img src="https://img2.meite.com/questions/202303/216419215338278.png" />（）</p><p>答 案：<img src="https://img2.meite.com/questions/202303/2164192163a3952.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202303/216419216d26ec4.png" /><img src="https://img2.meite.com/questions/202303/216419217fd3c42.png" /><img src="https://img2.meite.com/questions/202303/216419218b17310.png" /><img src="https://img2.meite.com/questions/202303/2164192192f3ecc.png" /> ps：根据本题的结构特征，容易想到凑微分<img src="https://img2.meite.com/questions/202303/21641921ac8d002.png" />  </p><p>2、设<img src="https://img2.meite.com/questions/202212/0863914005d5648.png" />，则<img src="https://img2.meite.com/questions/202212/08639140126f2fb.png" />（）</p><p>答 案：<img src="https://img2.meite.com/questions/202212/0863914020e19f3.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202212/086391402e77855.png" /></p><p class="introTit">简答题</p><p>1、<img src="https://img2.meite.com/questions/202404/22662627b17bf68.png" /></p><p>答 案：<img src="https://img2.meite.com/questions/202404/22662627cc472e7.png" /><img src="https://img2.meite.com/questions/202404/22662627cfe103c.png" /></p><p>2、计算<img src="https://img2.meite.com/questions/202204/256266681e38a4b.png" /></p><p>答 案：<img src="https://img2.meite.com/questions/202204/2562666955ecf07.png" /><img src="https://img2.meite.com/questions/202204/256266696a949be.png" /></p>