解题方法
1 . 已知函数
.
(1)求不等式
的解集;
(2)若关于
的方程
无实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41bb86452018de273e26496c714bcf2.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e661afc1ba382f0377c914e9ba6021c8.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e764c4a8ad3a55e136666d45f1f8fae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
2 . 已知函数
.
(1)求不等式
的解集;
(2)若直线
与
的图象所围成的三角形的面积为
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eebdae2dcdc7685152004165768b732f.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b45f8224a638bb503ccb01749cfeb1.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae077b198c3e6a891ca7c5eb6d53482a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7163395f9aaa29be7f6b3106ba48b744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
3 . 已知函数
,实数
满足
.
(1)解不等式
;
(2)证明:对任意实数
,使
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41704e782a18e4fc47cda11f4df5c4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6fae71c162e7be027a9b30a9187813.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a075dce77c9a6b964a8a3fc1ee6e8c.png)
(2)证明:对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a246b114e01128ed13a7d0798775d205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd2fa1502128fd34965a4a370f1eaed4.png)
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4 . 已知
,且
.
(1)求
的最小值m;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a521891098b625f372ff648d110afe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a78be779a807b53897bfeea6c8e4a1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa629b250bb3e84a30472721dd687dd5.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72544819df06031b061214aa0ebd3071.png)
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2卷引用:四川省成都市第七中学2024届高三下学期热身考试数学(文)试卷
名校
解题方法
5 . 已知函数
的最小值是
.
(1)求
的值;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b6c6897ea1463e25c6e25d5120c50f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26a9cd5393e7818121a7436783065c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12aa95f3db3a2b0d20f200c9a8b36959.png)
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解题方法
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffead0b0c68e8f023cf5ae0a7ba90936.png)
(1)当
时,求不等式
的解集;
(2)若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffead0b0c68e8f023cf5ae0a7ba90936.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a075dce77c9a6b964a8a3fc1ee6e8c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80fed8e87215b97c3b8bba07274159d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
7 . 已知函数
.
(1)求
的最小值;
(2)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec0b963b90847f531c4d16568ca7f667.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03fc1cd2baabbf8afea25478e1258237.png)
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8 . 已知
,
,
.
(1)当
时,求
的解集;
(2)若关于
的不等式
的解集为
,
的解集为
,若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ead9e67e1b855662553f1313055392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176c4a9de5a11fa2574fb00cd316a8db.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0db2c49919467a2e14540f2aabd05cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04bbcc3eb28e550b30e7ba6eaa09fe8f.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47a0b04c3da1ad31cccd905a575b151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a2c01ac2a7f6ad7e03cb7a61daefab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
9 . 已知函数
的最小值是m.
(1)求m的值;
(2)若
,
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a7b2dc826e500e362c22ddb6bfb39c8.png)
(1)求m的值;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab04de6651256f6281e9f4c1dc3c7955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054d00a127a585f7401a05d5351c6e37.png)
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名校
解题方法
10 . 已知函数
,
的最大值是
.
(1)求
的值;
(2)若
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b579f06fb171212d46ff13b34c799cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a895920706f9f39d1b48ab42e09923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bf140abb1d26b46f979f693fe71e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b56bfd6d391021a360e4b214de44b33c.png)
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