2024年成考专升本《高等数学二》每日一练试题09月08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/202408/1966c3036f87086.png" />（）。  </p><ul><li>A：<img src='https://img2.meite.com/questions/202408/1966c30373e9eba.png' /></li><li>B：<img src='https://img2.meite.com/questions/202408/1966c3037808377.png' /></li><li>C：<img src='https://img2.meite.com/questions/202408/1966c3037c8a593.png' /></li><li>D：<img src='https://img2.meite.com/questions/202408/1966c303830bc61.png' /></li></ul><p>答 案：A</p><p>2、设函数z＝f(x,y)在点<img src="https://img2.meite.com/questions/202212/0763904249e31fc.png" />存在一阶偏导数，则<img src="https://img2.meite.com/questions/202212/076390425670ed8.png" />（）.</p><ul><li>A：<img src='https://img2.meite.com/questions/202212/0763904260d7a98.png' /></li><li>B：<img src='https://img2.meite.com/questions/202212/076390426a33eb4.png' /></li><li>C：<img src='https://img2.meite.com/questions/202212/0763904274e2a12.png' /></li><li>D：<img src='https://img2.meite.com/questions/202212/076390427fc416b.png' /></li></ul><p>答 案：B</p><p>解 析：二元函数偏导数的定义式<img src="https://img2.meite.com/questions/202212/0763904295cfb2a.png" />.</p><p class="introTit">主观题</p><p>1、证明：当x＞0时，<img src="https://img2.meite.com/questions/202212/07638ffcd485955.png" /></p><p>答 案：证：令<img src="https://img2.meite.com/questions/202212/07638ffce6cc36a.png" />，<img src="https://img2.meite.com/questions/202212/07638ffcf78e460.png" />，令<img src="https://img2.meite.com/questions/202212/07638ffd0756606.png" />，得x＝0，f(0)=0，当x＞0时，f'(x)＜0，故函数单调递减，<img src="https://img2.meite.com/questions/202212/07638ffd5638022.png" />，则<img src="https://img2.meite.com/questions/202212/07638ffd669c31f.png" />．令<img src="https://img2.meite.com/questions/202212/07638ffd7859f24.png" />，<img src="https://img2.meite.com/questions/202212/07638ffd868ace9.png" />，令<img src="https://img2.meite.com/questions/202212/07638ffd960cd43.png" />，得x＝0，g(0)=0，当x＞0时，f'(x)＜0，故函数单调递减，f(x)＜f(0)=0，则<img src="https://img2.meite.com/questions/202212/07638ffde725bf7.png" />．综上得，当x＞0时，<img src="https://img2.meite.com/questions/202212/07638ffdf606f05.png" />．</p><p>2、甲乙两人独立地向同一目标射击，甲乙两人击中目标的概率分别为0.8与0.5，两人各射击一次，求至少有一人击中目标的概率．</p><p>答 案：解：设A＝{甲击中目标}，B＝{乙击中目标），C＝{目标被击中）则P（C）＝P（A十B）＝P（A）＋P（B）－P（AB）<br />＝P（A）＋P（B）－P（A）P（B）<br />＝0.8＋0.5－0.8×0.5<br />＝0.9．</p><p class="introTit">填空题</p><p>1、设y=sinx,则<img src="https://img2.meite.com/questions/202303/21641914679182e.png" />=（）  </p><p>答 案：-sinx</p><p>解 析：由y=sinx，且<img src="https://img2.meite.com/questions/202303/21641914a1d12f4.png" />则<img src="https://img2.meite.com/questions/202303/21641914b136fb6.png" />=sin(5π+x)=sin(π+x)=-sinx</p><p>2、已知函数<img src="https://img2.meite.com/questions/202212/06638ed9925d034.png" />在x＝0处连续，则a＝（）．</p><p>答 案：2</p><p>解 析：<img src="https://img2.meite.com/questions/202212/06638ed9a417a66.png" />，又f(x)在x＝0处连续，所以<img src="https://img2.meite.com/questions/202212/06638ed9bb85d4f.png" />．</p><p class="introTit">简答题</p><p>1、计算<img src="https://img2.meite.com/questions/202212/06638eb43edc03c.png" />  </p><p>答 案：由洛必达法则有<img src="https://img2.meite.com/questions/202212/06638eb44c28870.png" />  </p><p>2、<img src="https://img2.meite.com/questions/202408/2066c40a1d91b94.png" />  </p><p>答 案：<img src="https://img2.meite.com/questions/202408/2066c40a21428d8.png" /></p>