解题方法
1 . 设不等式
的解集为M,且
.
(Ⅰ)试比较
与
的大小;
(Ⅱ)设
表示数集A中的最大数, 且
, 求h的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a63d0250e2d28d393ed1ec25c42cf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cf8ef905453bbfc1e48984e87da9b9b.png)
(Ⅰ)试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdaba8b1591046933f2f725b6b1bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b73fefa3b1d5df3a688c1e5de71b659c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853b67d08166ff52b1a03effd8802176.png)
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解题方法
2 . 命题甲:关于
的不等式
的解集是空集.命题乙:指数函数
随着
增大而减小.
(1)若命题甲、命题乙中至少有一个真,求实数
的取值范围;
(2)当命题甲是假命题且命题乙为真命题时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c01a13ec34f954d237f72aa56a4a5388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bece79fa8dae9f21557e485590bb602c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)若命题甲、命题乙中至少有一个真,求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当命题甲是假命题且命题乙为真命题时,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853eca21bcd065961ddda3246b866120.png)
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解题方法
3 . 设函数
,不等式
的解集为M,a,
且
,
.
(1)证明:
;
(2)若对任意
恒有
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0022a58c849092f40b37f0d4bd27c491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e02125e0a1f3cda39742b765baa74c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab92728b35ed5798e07a2b0095bfcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03b011f69dfc5262a3d82f64676739b.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a964f66da41b8153cfcc6e3f826251.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29aef458f2367b76432719f6f56275d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3662da916f298db95206fd27b17f541.png)
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4 . (1)比较1与
的大小;
(2)求方程组
的解集;
(3)已知数轴上,
,
,且线段
的中点到原点的距离大于5,求x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d4ceb780d147ef10d3eaf29dda5327.png)
(2)求方程组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87287dc7ef7a0acb1678050972a30ee6.png)
(3)已知数轴上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b292af348189396a6a163965e34640.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5636bb94366afcddd8893e6fa7564ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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解题方法
5 . (1)已知不等式
的解集为M,若a、
,试比较
与
的大小;
(2)已知对于任意非零实数a和b,不等式
恒成立,求实数x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70be21d700725c712cd7a0f489480c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab92728b35ed5798e07a2b0095bfcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbc3eb703a37d9dd29d3825f1e9338e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7266b2ef457b8ddeee3fa2cc24022e.png)
(2)已知对于任意非零实数a和b,不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61604556a81ecdfc51c6dd1751a7a5e1.png)
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6 . 设不等式
的解集为
,且
,
.
(1)试比较
与
的大小;
(2)设
表示集合
中的最大数,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b3c5ce0fd88af42a4c0103070016e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582ad43edf388c096e7704d92340bf75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab92728b35ed5798e07a2b0095bfcc1.png)
(1)试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdaba8b1591046933f2f725b6b1bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dec63e6d30a41fcc8972397875bf46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a6af55a48a8e926e6133c4d33ecf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
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7 . (1)已知对于任意非零实数
和
,不等式
恒成立,试求实数
的取值范围;
(2)已知不等式
的解集为
,若
,试比较
与
的大小.(并说明理由)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6d9c60fa25bf789b48ef8ab5651996.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9942656b065269633af3859d6106b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a2b85186925658e66d8541a5645269e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbc3eb703a37d9dd29d3825f1e9338e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7266b2ef457b8ddeee3fa2cc24022e.png)
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8 . 已知函数
.
(1)若不等式
的解集为空集,求实数
的取值范围;
(2)若
且
,判断
与
的大小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3c0b15c0e9ad0e9348189cb160ab8f.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f33ba80eb69ecd8db970164ac7412f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d07fc9d3ca819de6d87d54d9ee0911e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7261334c5ce660d5236f1a837d485df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36576fd651dd88f5fd39a14848a0e9eb.png)
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