题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042601-15695.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-97563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-33504.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-58389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-22072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-59738.png)
(Ⅲ)证明不等式
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-27219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-65758.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-86900.png)
(Ⅱ)函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-22072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-55918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-99801.png)
(Ⅲ)由(Ⅱ)知,当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-51067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-22072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-59738.png)
从而可得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-96733.png)
得到
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-55721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-61408.png)
通过取
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-95127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-89906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-96400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-89906.png)
将上述n个不等式求和,得到:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-62521.png)
证得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-27219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-65758.png)
解析
试题分析:(Ⅰ)首先求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-43343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-17009.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-58389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042606-12990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-43343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042606-77138.png)
通过讨论
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042606-58417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042606-77553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-22072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-59738.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042606-28138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042607-78913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042607-62425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-22072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-55918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-99801.png)
(Ⅲ)由(Ⅱ)知,当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-51067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-22072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-59738.png)
从而可得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-96733.png)
得到
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-55721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-61408.png)
通过取
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-95127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-89906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-96400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-89906.png)
将上述n个不等式求和,得到:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-62521.png)
证得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-27219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-65758.png)
试题解析:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042607-52928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042607-57463.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-97563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042607-99100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-17009.png)
所以切线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042607-58623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-86900.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-58389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042606-12990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042606-77138.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042606-58417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042606-77553.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042606-77553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042608-55026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042608-32605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-22072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-59738.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042606-28138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042607-78913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042607-62425.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042608-17013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042608-67099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-22072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042609-82343.jpg)
函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-22072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-55918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-99801.png)
(Ⅲ)由(Ⅱ)知,当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-51067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-22072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042602-59738.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-96733.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-55721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-61408.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042604-95127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-89906.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042609-34232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-96400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-89906.png)
将上述n个不等式求和,得到:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042605-62521.png)
即不等式
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-27219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042603-65758.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042559-53221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042600-67001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042547-80801.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042547-54368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042548-19693.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042548-24342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042548-94863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042548-12304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042548-35211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042548-24342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042549-91124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042549-44353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042548-12304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042548-24342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042549-44353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042548-24342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042548-19693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042548-19693.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042525-23618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042525-65857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042526-63855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042526-88009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042526-43837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042525-65857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042525-23618.png)
(Ⅰ)已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042526-44489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042526-54941.png)
(Ⅱ)已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042527-35459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042527-25837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042527-37277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042527-11004.png)
(Ⅲ)已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042527-46470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042527-25837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042528-68751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042527-11004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042521-43906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042521-71092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042521-41595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042521-71092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042521-71092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042521-41595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042521-71092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042521-71092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042521-46870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042521-12761.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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