题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235117-10333.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235117-58446.gif)
(Ⅰ) 判断函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235117-85722.gif)
(Ⅱ) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235118-14342.gif)
(Ⅲ) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235118-20938.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235118-44177.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235118-82773.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235118-71083.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235119-98828.gif)
(Ⅱ)证明见解析
(Ⅲ)证明见解析
解析
(Ⅰ)定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235119-96083.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235119-26004.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235118-20938.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235119-58757.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235119-41990.gif)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235118-20938.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235119-86761.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235120-16421.gif)
则最大值
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235119-98828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235120-84321.gif)
(Ⅱ)要证明
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235118-14342.gif)
只
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235120-69332.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235120-72789.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235120-32756.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235121-45329.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235121-95708.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235121-14747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235121-28941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235121-70726.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235122-74946.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235120-16421.gif)
因此,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235122-47246.gif)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235122-52077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235122-93238.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235122-20354.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235123-40873.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235123-49070.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235123-20688.gif)
(Ⅲ)由标准正态分布
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235123-89320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235118-82773.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235123-34793.gif)
则由(Ⅱ)得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235124-25030.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235124-10259.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235118-20938.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235118-82773.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235118-71083.gif)
核心考点
试题【(本小题满分12分)函数.(Ⅰ) 判断函数的奇偶性,并求其最大值;(Ⅱ) 求证:;(Ⅲ) 求证:的图象与轴所围成的图形的面积不小于.】;主要考察你对函数的奇偶性与周期性等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235107-99026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235107-78312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235107-42849.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235107-50391.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235108-85279.gif)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235108-33594.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235108-29127.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235108-72486.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235109-11129.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235105-17547.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235106-78921.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235106-18961.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235106-33075.gif)
A.1 | B.2 | C.3 | D.5 |
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235100-70427.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235100-96564.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235100-13987.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235101-70506.gif)
(1) 求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235101-90364.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235100-70427.gif)
(2) 若关于
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235101-76621.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235101-41946.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235101-80633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235055-60569.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818235052-49554.gif)
A.3 | B.1 | C.-1 | D.-3 |
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