题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041755-88971.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041755-32194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041755-77516.png)
(Ⅱ)对任意的实数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041755-14478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041756-70496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041756-27203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041756-76811.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041756-32417.png)
解析
(1)中,根据二项式系数的性质可知,二项式系数的最大项取决于幂指数为奇数还是偶数来得到
(2)中利用均值不等式的思想,表示出
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041757-80299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041757-35778.png)
(Ⅰ)解:展开式中二项式系数最大的项是第3项,这项是
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041756-32417.png)
(Ⅱ)证法一:因
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041757-73422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041757-35778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041757-11473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041757-65596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041758-49179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041758-60363.png)
证法二:
因
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041757-73422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041757-35778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041757-11473.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041758-46840.png)
故只需对
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041758-78067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041758-16229.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041759-62640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041759-99237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041759-75473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041759-20646.png)
因为当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041800-11147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041800-35842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041800-46126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041800-52107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041801-36721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041800-46126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041759-20646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041800-46126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041801-37304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041801-69939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041802-14062.png)
从而有
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041802-94256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041802-58910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041802-36257.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041802-71772.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041718-95535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041718-76229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041719-21463.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041655-55525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041655-51987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041655-21131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041656-97966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041656-83921.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041619-17273.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041619-41773.png)
(2)若存在
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041620-19128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041620-87500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041620-44838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041609-11497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041609-15678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041609-33658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041610-95877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205041553-61559.png)
A.![]() | B.![]() ![]() | C.![]() | D.![]() |
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