2024高三·全国·专题练习
1 . (1)已知
,求证
;
(2)若将问题(1)中的数1换成任意正数
,命题是否成立,请说明理由;
(3)在问题(1)中,若
,请给出
的一个几何解释.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0e9b3dcb25156d84ba8f8f02ae1771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/510133d8effcc74bbf3ada029fd876b8.png)
(2)若将问题(1)中的数1换成任意正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)在问题(1)中,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c179c8c016cd2744ae1b947b7bc7486b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f7aba21067fce96fe2012caa198030.png)
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真题
2 . 已知
,函数
.设
,记曲线
在点
处的切线为l.
(1)求l的方程;
(2)设l与x轴交点为
.证明:
①
;
②若
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b6b83fc34793efda8e49ec70f974869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742b07c3c735c8a257f30b493a498485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8674b8c449a74c37fef3407f2ffcd582.png)
(1)求l的方程;
(2)设l与x轴交点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb652143b43cc9439a347b2b1dc5cf6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab69f3e93029f719145775bac23bbbeb.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc6c3352d5ef4d3c1cc152fe789d6f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7014374a3d09166425f7a8d79bf1c72c.png)
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名校
解题方法
3 . 已知
,
,且
.
(1)证明:
;
(2)若不等式
对任意
恒成立,求m的取值范围.
![](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/4a7dbc702617c765a573961953cc0901.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a909d65741563c842a45302c838b2a8.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc421f6b479e445156f799d7d3512393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
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2022-12-28更新
|
1055次组卷
|
13卷引用:专题22不等式选讲
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名校
解题方法
4 . 已知函数满足
.
(1)根据函数单调性的定义,证明
在区间
上单调递减,在区间
上单调递增;
(2)令
,若对
,
,都有
成立,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3f58722394cad3df7234b543be4587.png)
(1)根据函数单调性的定义,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee48ecba71465503cc47c987deaaa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673207f6b77b8192d25463d071737b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18460a96aebeb7b0a9963f476893f30d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b559fcc187fad2a90c2e4b76d2726493.png)
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2022-11-13更新
|
319次组卷
|
5卷引用:专题19 函数的基本性质(3)
名校
5 . 利用拉格朗日(法国数学家,1736-1813)插值公式,可以把二次函数
表示成
的形式.
(1)若
,
,
,
,
,把
的二次项系数表示成关于f的函数
,并求
的值域(此处视e为给定的常数,答案用e表示);
(2)若
,
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5457d763fd9698e27fbcc1ef6d53f00a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb5bac75f36bb1dc5c8190d4dbe681d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf94d263ea1e5ddad405ccbc1eb2a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f6db131eb532855af41d5e84ad22cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d0667df710a11c9f9f073babe66e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d0667df710a11c9f9f073babe66e7a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27763d65ec630511141303dad69545b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0e86caa2ab1bd37b67efe864815c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68982e0dd0bb3d87b344d23df4c2213.png)
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