2024年成考专升本《高等数学二》每日一练试题09月27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、设<img src="https://img2.meite.com/questions/202212/06638ea86688040.png" />为连续函数，则a＝（）.</p><ul><li>A：<img src='https://img2.meite.com/questions/202212/06638ea8727f6b7.png' /></li><li>B：<img src='https://img2.meite.com/questions/202212/06638ea87b84e87.png' /></li><li>C：2</li><li>D：1</li></ul><p>答 案：A</p><p>解 析：因为f(x)在x＝2连续，所以<img src="https://img2.meite.com/questions/202212/06638ea88e89c3f.png" /><img src="https://img2.meite.com/questions/202212/06638ea8a81a818.png" />故a＝<img src="https://img2.meite.com/questions/202212/06638ea8727f6b7.png" />.</p><p>2、已知函数y＝f(x)在实数集上恒有<img src="https://img2.meite.com/questions/202212/06638ee2ed266a4.png" />则曲线y＝f(x)的图象（ ）．  </p><ul><li>A：单调上升且上凹</li><li>B：单调下降且上凹</li><li>C：单调上升且上凸</li><li>D：单调下降且上凸</li></ul><p>答 案：A</p><p>解 析：<img src="https://img2.meite.com/questions/202212/06638ee313d864f.png" />故单调上升； 令<img src="https://img2.meite.com/questions/202212/06638ee32530c88.png" />，即<img src="https://img2.meite.com/questions/202212/06638ee3300821c.png" />分别在<img src="https://img2.meite.com/questions/202212/06638ee3390d4dd.png" />取<img src="https://img2.meite.com/questions/202212/06638ee3415a3c7.png" /><img src="https://img2.meite.com/questions/202212/06638ee348b84fe.png" />，则<img src="https://img2.meite.com/questions/202212/06638ee353e2067.png" /><img src="https://img2.meite.com/questions/202212/06638ee35ab3187.png" />可得<img src="https://img2.meite.com/questions/202212/06638ee3652a618.png" />，故函数上为凹。</p><p class="introTit">主观题</p><p>1、求由方程siny＋xe^y＝0确定的曲线在点（0，π）处的切线方程．</p><p>答 案：解：方程两边对x求导得<img src="https://img2.meite.com/questions/202212/07638ff644b304e.png" />得<img src="https://img2.meite.com/questions/202212/07638ff6525e5d7.png" />所以<img src="https://img2.meite.com/questions/202212/07638ff660f27da.png" />,故所求切线方程为y－π＝e^π（x－0）,即e^πx－y＋π＝0</p><p>2、求二元函数<img src="https://img2.meite.com/questions/202212/0863914c3c42e47.png" />的极值．</p><p>答 案：解：令<img src="https://img2.meite.com/questions/202212/0863914c4ae5571.png" />解得驻点<img src="https://img2.meite.com/questions/202212/0863914c56c0584.png" />A＝<img src="https://img2.meite.com/questions/202212/0863914c659e1b3.png" />，<img src="https://img2.meite.com/questions/202212/0863914c76d30c9.png" />，<img src="https://img2.meite.com/questions/202212/0863914c8597851.png" />，<img src="https://img2.meite.com/questions/202212/0863914c9497b8a.png" />，且A＞0．所以在点<img src="https://img2.meite.com/questions/202212/0863914cae2ec45.png" />处函数f（x，y）取极小值，极小值为<img src="https://img2.meite.com/questions/202212/0863914cc316554.png" /></p><p class="introTit">填空题</p><p>1、<img src="https://img2.meite.com/questions/202212/06638ed902c210e.png" />（）．</p><p>答 案：2</p><p>解 析：<img src="https://img2.meite.com/questions/202212/06638ed913181a5.png" />所以a=2.</p><p>2、<img src="https://img2.meite.com/questions/202408/1966c2efd05979b.png" />。  </p><p>答 案：<img src="https://img2.meite.com/questions/202408/1966c2efd5a0867.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202408/1966c2efda1dd99.png" /></p><p class="introTit">简答题</p><p>1、计算<img src="https://img2.meite.com/questions/202212/07639001b8236a7.png" />  </p><p>答 案：设x＝sint，dx＝costdt， 所以<img src="https://img2.meite.com/questions/202212/07639001d9da710.png" />  </p><p>2、<img src="https://img2.meite.com/questions/202408/1966c2aef41f549.png" />  </p><p>答 案：本题主要考查商的导数计算。 <img src="https://img2.meite.com/questions/202408/1966c2aef917468.png" />  </p>