名校
1 . 已知方程
有唯一实数解,则实数
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5410806b0e8d9a94b5d875355be0115d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
2 . 设函数
.
(1)若
,求
在
处的切线方程
(2)若
,
,求
的取值范围
(3)若对任意的
,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6daaf7811f4d7a65b9d922bf8dd518bf.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/045748e3e58bfc29cf00ea0b80d2d56b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92119b7b7c059a7e9ad0489329a51c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec72ca557aa4229ee871628ffcf0d8a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2033d35911865ead85db01936a3b37a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 已知
与
的图像上恰有两对关于
轴对称的点,则
的取值范围为_____________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e203fd8fc60b9010ae52f5d0ba0378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16db42a4c86f77e3262889bede7eea95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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4 . 在同一平面直角坐标系内,函数
及其导函数
的图象如图所示,已知两图象有且仅有一个公共点,其坐标为
,那么下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851c68ef2e0703706f3b528daa902eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4772c835cbe626040ecc4df30e6f0ccc.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 已知函数
,曲线
在点
处的切线与
轴相交于点
.
(1)求
的值;
(2)求
在区间
上的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b788482b243498329748b0cc2f72a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d06e33d079ac1649ee5eea8f61de7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c49350d67653f4fad39dcadec2460c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9099a75c433e97bbe05052a00110571.png)
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解题方法
6 . 已知函数
,若
,
,则实数k的最大值是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445cf059904978fbd30c298b6037907a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2939abf9f1755ea304eeb1e73063cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6700237e42df2f85392e4244ba0302.png)
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2024-05-08更新
|
401次组卷
|
2卷引用:天津市静海区第一中学2023-2024学年高二下学期3月学生学业能力调研数学试卷
7 . 已知函数
,
,
.
(1)求函数
的导数;
(2)若对任意的
,
,使得
成立,求a的取值范围;
(3)设函数
,若在区间
上存在零点,求a的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29e7afe826d90b67c8476b6a8ce60e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ddac37d332169a34598a63b4634b46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc55062abcda348cb4cf9837e2ab936d.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1760522e30613a463766f77d936429e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17641d15644d5fb2c79fd1016b21520f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6154e00013d9dee84c0e941f676ea9.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941ef382dc2543294af39d63cb550686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e1fcca51be2f5fea9bb06d0146fa50.png)
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解题方法
8 . 函数
在区间
上的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09e4edfbd52e9797ff1d7edbc15a17c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bccd6a6e85bdf500218a3e75b31f3c.png)
A.-1 | B.1 | C.![]() | D.![]() |
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9 . 已知函数
,下列命题不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e6a22797c8f01b9c05925440c6151f0.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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解题方法
10 . 已知
,
,使得
成立,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0919c2dfa75ecc2b69102c445073eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911d77a96eed2aeccab27c4c59d357d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8c626afbc95213849e8f122d9b1a13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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