1 . 已知命题
对于
成立,命题
关于k的不等式
成立.
(1)若命题p为真命题,求实数k的取值范围;
(2)若命题p是命题q的必要不充分条件,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8afe3bc2541382ef1c17ee8532b366bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc08dfa75b0dd54004ef8ea8c39e5530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9dab20d7facf86b29a8c838e436a16.png)
(1)若命题p为真命题,求实数k的取值范围;
(2)若命题p是命题q的必要不充分条件,求实数m的取值范围.
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解题方法
2 . 设函数
,其中
.
(1)若命题“
”为假命题,求实数
的取值范围;
(2)若函数
在区间
内恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa1f9cde354a83e85eb252d97d383c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
(1)若命题“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf44939777c747005f08ddc790f22b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f8bd074415eea5bb0764011d78a908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
3 . 已知函数
.
(1)解关于
的不等式:
;
(2)命题“
”是真命题,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac42361cfbff80650c8b65a087098efe.png)
(1)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66d61d5f66d68b4c4a2a25fd7103621.png)
(2)命题“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f450178c1d9b51b43eb2f42648454008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 已知
,命题p:
,
;命题q:
,
.
(1)若命题p为假命题,求a的取值范围;
(2)若p和q均为真命题,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8645952ea14b25443f411d39bdec641e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61901f0c23f1994acb34bd8c0c793e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5e14f6464b4aeadb50f60b75d332b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3729c862a5464eb647f06c43a6279187.png)
(1)若命题p为假命题,求a的取值范围;
(2)若p和q均为真命题,求a的取值范围.
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解题方法
5 . 设函数
,其中
.
(1)若命题“
,
”为假命题,求实数
的取值范围;
(2)判断
在区间
上的单调性,并用函数单调性的定义证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d2c4d804f4c0120d38e2fc897a9c4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
(1)若命题“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ccd7af9298cd5ff19d8866fedb42ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ce82779a834a6871c96515eaaa5571.png)
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6 . 已知命题p:“
,
”,命题q:“
,
没有实数根”.若p与q均为真命题,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8645952ea14b25443f411d39bdec641e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4df9e15031d426ae96cf205dcd06ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36bcb4df710cf7fc5a4159380ae5451e.png)
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7 . (1)“
,使得方程
有两个不同的实数解”是真命题,求集合A.
(2)若命题“
,
”为真命题,求实数a的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5581fc420e0d340f8948817b5ad235.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc75dcb764833ca2a1eeb3d533bdf41c.png)
(2)若命题“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659f6511c71f5b1bdf784d865934c33d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/badab08664c0a5fd3d6da6c46a987ffc.png)
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名校
8 . 设命题 p:对任意
,不等式
恒成立; 命题q:存在
, 使得不等式
成立.
(1)若p为真命题,求实数 m 的取值范围;
(2)若命题p,q至少有一个是真命题,求实数 m 的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538193a4717d564c01145e82314c2d1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d74c3f71d4c7a974814b024eabbc1622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f0ca536621ec8db02707ba65917029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402e03456d9a208f5c41785e39f31092.png)
(1)若p为真命题,求实数 m 的取值范围;
(2)若命题p,q至少有一个是真命题,求实数 m 的取值范围.
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解题方法
9 . (1)已知集合
,
.求能使
成立的实数
的取值范围;
(2)已知命题
,
为假命题,求实数
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe06c5fec138ea16d554839caec51ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d08b3e0b73ef478264b6ec14c41443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9d50619b779c1056602f46b2a95e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83e82639a9124007e27fbec3681807c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072c300a8d75385dbe53caeb2514fa00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
10 . 是否存在整数m,使得命题“
”是真命题?若存在,求出m的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4438732e9c9090d49b8945623b7140f0.png)
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