2024年成考专升本《高等数学二》每日一练试题08月15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>2、下列等式中成立的是（）</p><ul><li>A：<img src='https://img2.meite.com/questions/202212/0763902c0a65152.png' /></li><li>B：<img src='https://img2.meite.com/questions/202212/0763902c15e917b.png' /></li><li>C：<img src='https://img2.meite.com/questions/202212/0763902c26761a1.png' /></li><li>D：<img src='https://img2.meite.com/questions/202212/0763902c31733ef.png' /></li></ul><p>答 案：D</p><p>解 析：AD两项，<img src="https://img2.meite.com/questions/202212/0763902c3d17d53.png" />；BC两项，<img src="https://img2.meite.com/questions/202212/0763902c4e157a0.png" /></p><p class="introTit">主观题</p><p>1、计算<img src="https://img2.meite.com/questions/202212/07639039f5ae5b6.png" />．</p><p>答 案：解：<img src="https://img2.meite.com/questions/202212/0763903a0ad1fb5.png" /><img src="https://img2.meite.com/questions/202212/0763903a1c62dae.png" />．</p><p>2、计算<img src="https://img2.meite.com/questions/202212/06638e9ca8b67fc.png" />．</p><p>答 案：解：<img src="https://img2.meite.com/questions/202212/06638e9cb5ca788.png" /></p><p class="introTit">填空题</p><p>1、<img src="https://img2.meite.com/questions/202303/216419215338278.png" />（）</p><p>答 案：<img src="https://img2.meite.com/questions/202303/2164192163a3952.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202303/216419216d26ec4.png" /><img src="https://img2.meite.com/questions/202303/216419217fd3c42.png" /><img src="https://img2.meite.com/questions/202303/216419218b17310.png" /><img src="https://img2.meite.com/questions/202303/2164192192f3ecc.png" /> ps：根据本题的结构特征，容易想到凑微分<img src="https://img2.meite.com/questions/202303/21641921ac8d002.png" />  </p><p>2、若<img src="https://img2.meite.com/questions/202212/07639034345b695.png" />则a＝()．</p><p>答 案：1</p><p>解 析：<img src="https://img2.meite.com/questions/202212/076390344195c28.png" />，所以a＝1．</p><p class="introTit">简答题</p><p>1、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><p>2、设随机变量X的概率分布为：<img src="https://img2.meite.com/questions/202212/06638eda161b9ed.png" /> 求X的期望、方差以及标准差．</p><p>答 案：<img src="https://img2.meite.com/questions/202212/06638eda2e62e11.png" /> <img src="https://img2.meite.com/questions/202212/06638eda375c467.png" /></p>