名校
解题方法
1 . 已知函数
对任意的实数m,n都有
,且当
时,有
恒成立.
(1)求
的值;
(2)求证
在R上为增函数;
(3)若
,
,对任意的
,则关于x的不等式
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053e4e1dc1431145c998c014b8fc0c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
(2)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9bf4ec57e9172349be55e4527214acc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2188e898a6af08a1e4f4001001194bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab099277f1ca651f5acca46ca054844c.png)
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名校
2 . 已知单位向量
、
夹角为60°,向量
,
,函数
,函数
.
(1)求出
并解方程
;
(2)设
,
,证明
,求出
;
(3)设数列
中,
,
,
,求
的取值范围,使
对任意
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8315ec34019d719771152be2252106e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf39ca3294f5520518dd4f1c0609876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2795c23d9ae250f97272fe45647b619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c68ae32a33b25a7da4a22375aeb97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5acd92c11b40a6a7df2862ee780fd19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d178399b685d411fc08169d8e4dd102.png)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907e4ba6d5f2eea68442def1911957fe.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998d1117b68d345ad988e86d1ec7724b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acec5abbaf06572719eb3e438cbee96f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7268ee120ea28a987f9e0eebf859f067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84323e71222a3dd2ddf73bc9c654c01b.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8cc56056a35396d9b94bee47a5b17c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c378b096c02a762afd59dfb0a3574e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17bc84f50a043f6bfb4b8e35460a1fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
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