题目内容
(本题满分14分)设函数
,其中向量
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846809697.gif)
(1)求函数
的最小正周期和单调递增区间
(2)当
时,
恒成立,求实数
的取值范围
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846777471.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846793506.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846809697.gif)
(1)求函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846840270.gif)
(2)当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846871493.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846887380.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846918204.gif)
依题意
又
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846809697.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846980128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847011770.gif)
=
=
……4分
设函数
的最小正周期为T,则T=
……1分
当
时,函数单调递增故解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847214801.gif)
函数的单调递增区间为[
……3分
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847386193.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847401637.gif)
故![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847433693.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846980128.gif)
3分
依题意 当
时,
恒成立
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846980128.gif)
解得
3分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846777471.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846793506.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846809697.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846980128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847011770.gif)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847027674.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847043683.gif)
设函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846840270.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847167196.gif)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847199926.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847214801.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846980128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847277743.gif)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847355183.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847370468.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847386193.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847401637.gif)
故
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847433693.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846980128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847464594.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847495115.gif)
依题意 当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847511503.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846887380.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155846980128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847573634.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847589418.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155847495115.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
练习册系列答案
相关题目