2024年成考专升本《高等数学二》每日一练试题08月18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、若f(x)的一个原函数为<img src="https://img2.meite.com/questions/202212/07639005951b41f.png" />，则下列等式正确的是（）</p><ul><li>A：<img src='https://img2.meite.com/questions/202212/07639005a4e09d7.png' /></li><li>B：<img src='https://img2.meite.com/questions/202212/07639005b299370.png' /></li><li>C：<img src='https://img2.meite.com/questions/202212/07639005be00fbe.png' /></li><li>D：<img src='https://img2.meite.com/questions/202212/07639005ca1c2d0.png' /></li></ul><p>答 案：B</p><p>解 析：根据不定积分的定义，可知<img src="https://img2.meite.com/questions/202212/07639005d963d7f.png" /></p><p>2、<img src="https://img2.meite.com/questions/202212/06638ea45cb9d2e.png" />（ ）．  </p><ul><li>A：0</li><li>B：1</li><li>C：<img src='https://img2.meite.com/questions/202212/06638ea47909679.png' /></li><li>D：<img src='https://img2.meite.com/questions/202212/06638ea47e449e5.png' /></li></ul><p>答 案：D</p><p>解 析：<img src="https://img2.meite.com/questions/202212/06638ea4950ac2c.png" /></p><p class="introTit">主观题</p><p>1、求函数f（x）＝<img src="https://img2.meite.com/questions/202212/07638ff69b36a43.png" />，在<img src="https://img2.meite.com/questions/202212/07638ff6ae2829e.png" />上的最大值和最小值．</p><p>答 案：解：<img src="https://img2.meite.com/questions/202212/07638ff6c1f170c.png" />，令<img src="https://img2.meite.com/questions/202212/07638ff6cf509c3.png" />，在<img src="https://img2.meite.com/questions/202212/07638ff6dedfa07.png" />内解得驻点为<img src="https://img2.meite.com/questions/202212/07638ff8c4bcb56.png" />，<img src="https://img2.meite.com/questions/202212/07638ff8d26be39.png" />，求出以上各点及端点处函数值<img src="https://img2.meite.com/questions/202212/07638ff8e86101a.png" />比较可得，f（x）在<img src="https://img2.meite.com/questions/202212/07638ff900ed53a.png" />上最大值为<img src="https://img2.meite.com/questions/202212/07638ff90ea6665.png" />，最小值为<img src="https://img2.meite.com/questions/202212/07638ff91e7759e.png" />．</p><p>2、计算<img src="https://img2.meite.com/questions/202212/05638d9d9ed2616.png" /></p><p>答 案：解：利用重要极限<img src="https://img2.meite.com/questions/202212/05638d9dacb2519.png" />，则<img src="https://img2.meite.com/questions/202212/05638d9dba38c4e.png" /></p><p class="introTit">填空题</p><p>1、设<img src="https://img2.meite.com/questions/202212/07638feeafa517e.png" />，则<img src="https://img2.meite.com/questions/202212/07638feebb1c2fa.png" />＝（）．</p><p>答 案：<img src="https://img2.meite.com/questions/202212/07638feec69f390.png" /></p><p>解 析：<img src="https://img2.meite.com/questions/202212/07638fef11167a1.png" /><img src="https://img2.meite.com/questions/202212/07638fef1e8392a.png" /></p><p>2、已知函数<img src="https://img2.meite.com/questions/202212/05638d666760032.png" />，则f(0)＝（）．</p><p>答 案：</p><p>解 析：<img src="https://img2.meite.com/questions/202212/05638d667e46811.png" />．</p><p class="introTit">简答题</p><p>1、计算<img src="https://img2.meite.com/questions/202303/206417fb91cb6ad.png" /></p><p>答 案：<img src="https://img2.meite.com/questions/202303/206417fb9f9dbfe.png" />（被积函数为偶函数）<img src="https://img2.meite.com/questions/202303/206417fbad33c66.png" /><img src="https://img2.meite.com/questions/202303/206417fbc814c98.png" /></p><p>2、从一批有10件正品及2件次品的产品中，不放回地一件一件地抽取产品．设每个产品被抽到的可能性相同。求直到取出正品为止所需抽取的次数X的概率分布。</p><p>答 案：<img src="https://img2.meite.com/questions/202204/2462651cccbe0ff.png" /><img src="https://img2.meite.com/questions/202204/2462651cdfecf00.png" /><img src="https://img2.meite.com/questions/202204/2462651ce6c152c.png" /></p>