1 . 已知函数
在
处取得极值.
(1)求实数a的值;
(2)若关于x的方程
在区间
上恰有两个不同的实数根,求实数t的取值范围;
(3)证明:对任意的正整数n,不等式
都成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ccd0083aafaa8d0dd3c48edd41b4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(1)求实数a的值;
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c25b2669c1130c028447eeabc39b55d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
(3)证明:对任意的正整数n,不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba6c7ec8f6c6127448a724e16b096ea5.png)
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名校
2 . 已知函数
.
(1)当
时,讨论
的单调性;
(2)令
,若
有两个不相等的实数根
.
(i)求a的取值范围;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c59ee61e811f2cbb69edcd7445e8d5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5466c28592d45ca35059382b351d583f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(i)求a的取值范围;
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0fd6297d9af0dbfaccd08a53054ec5.png)
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