题目内容
已知
在R上单调递增,记
的三内角
的对应边分别为
,若
时,不等式
恒成立.
(Ⅰ)求实数
的取值范围;
(Ⅱ)求角
的取值范围;
(Ⅲ)求实数
的取值范围.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951207594.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951222400.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951238291.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951253260.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951269383.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231329512851105.gif)
(Ⅰ)求实数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951300199.gif)
(Ⅱ)求角
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951316268.gif)
(Ⅲ)求实数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951331204.gif)
(1)
. (2)
,(3)
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951347295.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951363468.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951378445.gif)
(1)由
知
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951425133.gif)
在R上单调递增,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951456128.gif)
恒成立,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951456128.gif)
且
,即
且
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951456128.gif)
,
当
,即
时,
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951456128.gif)
时
,
时,
,即当
时,能使
在R上单调递增,
.
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951425133.gif)
,由余弦定理:
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951456128.gif)
,----5分
(3)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951425133.gif)
在R上单调递增,且
,所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951909923.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231329519241600.gif)
,---10分
故
,即
,
,即
,即
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951394590.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951409601.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951425133.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951441280.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951456128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951472437.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951456128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951503377.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951519251.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951534254.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951550434.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951456128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951581288.gif)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951597240.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951628280.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951643717.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951456128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951675227.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951690355.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951706229.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951690355.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951628280.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951441280.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951753305.gif)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951425133.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951784375.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951799816.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951456128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951363468.gif)
(3)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951425133.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951441280.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231329518931127.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951909923.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231329519241600.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951940625.gif)
故
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951955477.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951971500.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951987479.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132952002453.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132951378445.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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