题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-41012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-92777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-92777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-86729.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-97995.png)
(2)证明不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-69337.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-81049.png)
解析
试题分析:(1)由题设可得两个方程:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-50905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-21668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-35656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-97995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-69337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-61899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-62778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-76204.png)
试题解析:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-41012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042044-96645.png)
∵曲线C过
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-92777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-50905.png)
又∵曲线C在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-92777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-86729.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-21668.png)
联立①②解之得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042044-44320.png)
∴函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042042-97995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-81049.png)
(2)由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042044-59286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042044-64717.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042044-59683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-62778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042045-10348.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042045-35766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-62778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042045-74118.png)
∴函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042045-86543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042045-61643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042046-44813.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042046-80862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042043-76204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042046-54801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042046-51799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042047-86472.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042029-86294.png)
(1)如果
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042029-23625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042030-44414.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042030-44414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042030-98058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042030-19939.png)
(3)证明:当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042030-16466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042031-52995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042026-84847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042026-87958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042005-86689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042005-25577.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042005-19030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042005-75596.png)
(Ⅱ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042005-75596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042006-75940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042005-25577.png)
(Ⅲ)证明:曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042006-54825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042006-11985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042006-54825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042006-36513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018042007-45780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041950-91513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041951-28046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041951-51137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041951-23088.png)
(Ⅰ)用
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041951-16101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041951-20061.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041952-31279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041952-51847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041952-15666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041951-16101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041935-15637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041935-65866.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041935-80318.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041935-94555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041935-30731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041935-84442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041935-21631.png)
(Ⅲ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018041936-87366.png)
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