2024年成考专升本《高等数学二》每日一练试题06月21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/202212/06638eeb0a112ec.png" />则f（x）在点x＝0处（）.</p><ul><li>A：可导且<img src='https://img2.meite.com/questions/202212/06638eeb199d2a7.png' />＝0</li><li>B：可导且<img src='https://img2.meite.com/questions/202212/06638eeb1b04b30.png' />＝1</li><li>C：不连续</li><li>D：连续但不可导</li></ul><p>答 案：A</p><p>解 析：因为<img src="https://img2.meite.com/questions/202212/06638eeb2e653bc.png" />，所以，f（x）在x＝0处连续；又<img src="https://img2.meite.com/questions/202212/06638eeb4483efe.png" />所以f（x）在点x＝0处可导且<img src="https://img2.meite.com/questions/202212/06638eeb586decf.png" />＝0.</p><p>2、已知P(A)＝<img src="https://img2.meite.com/questions/202212/08639153fb41da0.png" />，P(B)＝<img src="https://img2.meite.com/questions/202212/0863915406d82bb.png" />，下列结论正确的是（）.</p><ul><li>A：P(AB)＝<img src='https://img2.meite.com/questions/202212/08639154146e9c3.png' /></li><li>B：若Ａ，Ｂ互斥，则P(AB)＝<img src='https://img2.meite.com/questions/202212/0863915415dc3e2.png' /></li><li>C：若A，B独立，则P(AB)＝<img src='https://img2.meite.com/questions/202212/08639154175bcc0.png' /></li><li>D：若A，B对立，则P(AB)＝<img src='https://img2.meite.com/questions/202212/08639154189c6ff.png' /></li></ul><p>答 案：C</p><p>解 析：互斥，则P(AB)＝0，P(A＋B)＝P(A)＋P(B)；A，B独立，则P(AB)＝P(A)×P(B)；A，B对立，则P(A)＋P(B)＝1.</p><p class="introTit">主观题</p><p>1、设z=f(x,y)是由方程<img src="https://img2.meite.com/questions/202212/0863914adb1350d.png" />确定的函数，求<img src="https://img2.meite.com/questions/202212/0863914ae82119e.png" />．</p><p>答 案：解：x，y是自变量，而z＝z（x，y）．等式两边对x求导得<img src="https://img2.meite.com/questions/202212/0863914afbe2347.png" />等式两边对y求导得<img src="https://img2.meite.com/questions/202212/0863914b0b42bf4.png" />解得<img src="https://img2.meite.com/questions/202212/0863914b19bd459.png" /></p><p>2、已知<img src="https://img2.meite.com/questions/202212/07639036e33c6d5.png" />，计算<img src="https://img2.meite.com/questions/202212/07639036f2e26db.png" /></p><p>答 案：解：<img src="https://img2.meite.com/questions/202212/0763903701a055b.png" /></p><p class="introTit">填空题</p><p>1、设函数<img src="https://img2.meite.com/questions/202212/05638d51837d16c.png" />在x＝0处连续，则a＝（）．</p><p>答 案：1</p><p>解 析：函数在x＝0处连续，则有<img src="https://img2.meite.com/questions/202212/05638d5198052e0.png" />，<img src="https://img2.meite.com/questions/202212/05638d51a981873.png" />，<img src="https://img2.meite.com/questions/202212/05638d51ba22b34.png" />，故a＝1．</p><p>2、<img src="https://img2.meite.com/questions/202212/05638d97afefc8d.png" />（）．</p><p>答 案：</p><p>解 析：由洛必达法则有<img src="https://img2.meite.com/questions/202212/05638d97c05d5c7.png" />．</p><p class="introTit">简答题</p><p>1、设<img src="https://img2.meite.com/questions/202204/246264fadbef105.png" />存在，<img src="https://img2.meite.com/questions/202204/246264fb61174de.png" /></p><p>答 案：<img src="https://img2.meite.com/questions/202204/246264fed311d67.png" /></p><p>2、设函数<img src="https://img2.meite.com/questions/202212/0763900106d1c67.png" />求常数a。使f(x)在点x=0处连续。  </p><p>答 案：<img src="https://img2.meite.com/questions/202212/0763900142438db.png" /> 要f(x)在点x=0处连续，则需<img src="https://img2.meite.com/questions/202212/076390015badfb6.png" />所以a=1.</p>