2024年成考专升本《高等数学二》每日一练试题05月29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、已知<img src="https://img2.meite.com/questions/202212/06638ee92dad126.png" />，则<img src="https://img2.meite.com/questions/202212/06638ee93baa212.png" />＝（）.</p><ul><li>A：<img src='https://img2.meite.com/questions/202212/06638ee9462495d.png' /></li><li>B：<img src='https://img2.meite.com/questions/202212/06638ee9519cd96.png' /></li><li>C：<img src='https://img2.meite.com/questions/202212/06638ee95a2bfca.png' /></li><li>D：<img src='https://img2.meite.com/questions/202212/06638ee96305d11.png' /></li></ul><p>答 案：B</p><p>解 析：因为<img src="https://img2.meite.com/questions/202212/06638eea0121449.png" />，所以<img src="https://img2.meite.com/questions/202212/06638eea0b32e71.png" />.</p><p>2、3个男同学与2个女同学排成一列，设事件A＝{男女必须间隔排列），则P（A）＝（）.</p><ul><li>A：<img src='https://img2.meite.com/questions/202212/086391525579f6a.png' /></li><li>B：<img src='https://img2.meite.com/questions/202212/086391526094171.png' /></li><li>C：<img src='https://img2.meite.com/questions/202212/08639152696c7db.png' /></li><li>D：<img src='https://img2.meite.com/questions/202212/0863915270f0825.png' /></li></ul><p>答 案：B</p><p>解 析：5人排成一列的排列总数为5!，男女必须间隔排列只有3个男的排在1，3，5的位置，2个女的排在2，4的位置，共有<img src="https://img2.meite.com/questions/202212/086391528632efa.png" />种排法，故<img src="https://img2.meite.com/questions/202212/08639152937aff7.png" />.</p><p class="introTit">主观题</p><p>1、计算<img src="https://img2.meite.com/questions/202212/05638d9e56ddb77.png" />．</p><p>答 案：解：设<img src="https://img2.meite.com/questions/202212/05638d9e64208c2.png" />，则dx＝2tdt．当x＝0时，t＝0；当x＝1时，t＝1．则<img src="https://img2.meite.com/questions/202212/05638d9e78cc817.png" /></p><p>2、函数z＝f(x，y)由<img src="https://img2.meite.com/questions/202212/0863914fe23e2f3.png" />所确定，求<img src="https://img2.meite.com/questions/202212/0863914fed6be0a.png" />．</p><p>答 案：解：方程两边关于x求偏导数，得<img src="https://img2.meite.com/questions/202212/086391502ded927.png" />即<img src="https://img2.meite.com/questions/202212/086391503c37b45.png" />．方程两边关于y求偏导数，得<img src="https://img2.meite.com/questions/202212/086391504eaf8c9.png" />即<img src="https://img2.meite.com/questions/202212/086391505b43a2a.png" />．</p><p class="introTit">填空题</p><p>1、若<img src="https://img2.meite.com/questions/202212/06638edb472fcb7.png" />存在，且<img src="https://img2.meite.com/questions/202212/06638edb55776c5.png" />则<img src="https://img2.meite.com/questions/202212/06638edb678307d.png" />（）．</p><p>答 案：－3</p><p>解 析：设<img src="https://img2.meite.com/questions/202212/06638edb758fc22.png" />＝A，对<img src="https://img2.meite.com/questions/202212/06638edb835eb08.png" />两边求x＝1处的极限得A＝3＋2A，解得A＝－3，即<img src="https://img2.meite.com/questions/202212/06638edb943e578.png" />＝－3．</p><p>2、<img src="https://img2.meite.com/questions/202212/0763903211a9f98.png" />，则a＝()．</p><p>答 案：1</p><p>解 析：<img src="https://img2.meite.com/questions/202212/076390321fb5d32.png" /></p><p class="introTit">简答题</p><p>1、设函数<img src="https://img2.meite.com/questions/202303/076406d89b38e25.png" />在x=0处连续，求a.  </p><p>答 案：因为f（x）在x=0处连续，所以<img src="https://img2.meite.com/questions/202303/076406e2df16532.png" />由于<img src="https://img2.meite.com/questions/202303/076406e2fa670e3.png" />所以a=2.</p><p>2、计算<img src="https://img2.meite.com/questions/202212/06638ed85f1bb2b.png" /></p><p>答 案：<img src="https://img2.meite.com/questions/202212/06638ed870e7e7d.png" /> 设<img src="https://img2.meite.com/questions/202212/06638ed877da168.png" />则<img src="https://img2.meite.com/questions/202212/06638ed87f9ff73.png" /><img src="https://img2.meite.com/questions/202212/06638ed884a7365.png" /></p>