题目内容
已知函数
(其中
且
,
为实常数).
(Ⅰ)若
,求
的值(用
表示);
(Ⅱ)若
且
对于
恒成立,求实数m的取值范围(用
表示).
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935118757.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935134399.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935149378.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935165283.png)
(Ⅰ)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935181543.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935227266.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935165283.png)
(Ⅱ)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935259386.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935274938.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935290500.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935165283.png)
(Ⅰ)当
时
,当
时,
. …………….2分
由条件可知,
,即
解得
…………4分
因为
…………..6分
(Ⅱ)当
时,
……………8分
即![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935539812.png)
因为
……10分
因为
所以![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935633768.png)
所以![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935649907.png)
故m的取值范围是![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935664652.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935352383.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935368516.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935383391.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935399719.png)
由条件可知,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935415566.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935430637.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935446535.png)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935493994.png)
(Ⅱ)当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935508509.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232019355241103.png)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935539812.png)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935571651.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935586928.png)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935602526.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935633768.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935649907.png)
故m的取值范围是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823201935664652.png)
略
![](http://thumb.zyjl.cn/images/loading.gif)
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