2024年成考专升本《高等数学二》每日一练试题05月23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、随机事件A与B为互不相容事件，则P(AB)＝（）.</p><ul><li>A：P(A)＋P(B)</li><li>B：P(A)P(B)</li><li>C：1</li><li>D：0</li></ul><p>答 案：D</p><p>解 析：事件A与B为互不相容事件，则两事件不可能同时发生，故P（AB）＝0.</p><p>2、<img src="https://img2.meite.com/questions/202212/0763900be25eb38.png" />（）</p><ul><li>A：<img src='https://img2.meite.com/questions/202212/0763900beb5cc78.png' /></li><li>B：<img src='https://img2.meite.com/questions/202212/0763900bf67d464.png' /></li><li>C：<img src='https://img2.meite.com/questions/202212/0763900c00dc353.png' /></li><li>D：<img src='https://img2.meite.com/questions/202212/0763900c08d1f95.png' /></li></ul><p>答 案：B</p><p>解 析：<img src="https://img2.meite.com/questions/202212/0763900c1a59be9.png" /></p><p class="introTit">主观题</p><p>1、求曲线y＝x²与直线y＝0，x＝1所围成的平面图形绕x轴旋转一周所得旋转体的体积V．</p><p>答 案：解：<img src="https://img2.meite.com/questions/202212/03638b113e559ed.png" /></p><p>2、计算<img src="https://img2.meite.com/questions/202212/06638ee0d87d280.png" /></p><p>答 案：解：<img src="https://img2.meite.com/questions/202212/06638ee0e4bb86f.png" /></p><p class="introTit">填空题</p><p>1、设<img src="https://img2.meite.com/questions/202212/07638fedd2b1493.png" />，f（x₀）＝5，则<img src="https://img2.meite.com/questions/202212/07638fede94ed85.png" />＝（）．</p><p>答 案：<img src="https://img2.meite.com/questions/202212/07638fedf537be5.png" /></p><p>解 析：因为<img src="https://img2.meite.com/questions/202212/07638fee129b5b1.png" />，f（x₀）＝5，所以<img src="https://img2.meite.com/questions/202212/07638fee23474e6.png" />，即<img src="https://img2.meite.com/questions/202212/07638fee3308298.png" />，所以<img src="https://img2.meite.com/questions/202212/07638fee3d9c6e9.png" />；因为<img src="https://img2.meite.com/questions/202212/07638fee516ece0.png" />所以<img src="https://img2.meite.com/questions/202212/07638fee685a767.png" />，即<img src="https://img2.meite.com/questions/202212/07638fee787cba9.png" />．</p><p>2、当x→0时，f（x）与sin2x是等价无穷小量，则<img src="https://img2.meite.com/questions/202212/05638d97d083de0.png" />（）．</p><p>答 案：1</p><p>解 析：根据等价无穷小定义，可知<img src="https://img2.meite.com/questions/202212/05638d97e363000.png" />．</p><p class="introTit">简答题</p><p>1、已知曲线<img src="https://img2.meite.com/questions/202303/216419246048f3b.png" />在点(1,2)处有水平切线，且原点为该曲线的拐点，求a,b,c的值，并写出此曲线的方程。  </p><p>答 案：<img src="https://img2.meite.com/questions/202303/2164192515baa08.png" /><img src="https://img2.meite.com/questions/202303/2164192520cbb96.png" /> 由已知条件得： <img src="https://img2.meite.com/questions/202303/2164192541ec9d6.png" /> 故b=0,a=-1，c=3，次曲线的方程为<img src="https://img2.meite.com/questions/202303/21641925650ce9b.png" />  </p><p>2、证明：<img src="https://img2.meite.com/questions/202303/206417fa32611db.png" /></p><p>答 案：令<img src="https://img2.meite.com/questions/202303/206417fa5d92774.png" />则<img src="https://img2.meite.com/questions/202303/206417fa64709ff.png" />由于此式不便判定符号，故再求出<img src="https://img2.meite.com/questions/202303/206417fa8f7819c.png" />又因<img src="https://img2.meite.com/questions/202303/206417fa9f5cd03.png" /><img src="https://img2.meite.com/questions/202303/206417faa4b9537.png" />所以f'(x)单调增加，故f'(x)>f'(4)=<img src="https://img2.meite.com/questions/202303/206417facca9272.png" />-8=8(2ln2-1)=8(ln4-1)>0, 得到f(x)单调增加，故f(x)>f(4),即<img src="https://img2.meite.com/questions/202303/206417fb29350f8.png" />因此<img src="https://img2.meite.com/questions/202303/206417fb3703866.png" /></p>