名校
解题方法
1 . 已知函数
,
,则下列说法正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bd8a100f995d01627c3cb6a2ae8c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b9d6be01fc9d47f5965f32d767b742.png)
A.函数![]() ![]() |
B.当![]() ![]() ![]() |
C.若函数![]() ![]() ![]() |
D.若不等式![]() ![]() ![]() |
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2 . 已知
,则在下列关系①
;②
;③
;④
中,能作为“
”的必要不充分条件的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd00e2f6802c99fb624aa77ebe17d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72f0a62b1a8614acae64570d8bf1170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b973e2ec0d256343c57ce0c3cd80ab2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65eb4d879e3e80d3195b56b303e331c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485a2d99320384a0857b00ce9ab9e990.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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3 . 设双曲线
,直线
与双曲线
的右支交于点
,
,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fcd560996764805b57994a97c26e56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.双曲线![]() |
B.离心率最小时双曲线![]() ![]() |
C.若直线![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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4 . 已知函数
(
为常数)的图象上存在四个点
,过
的切线为
,其中
,且
围成的图形是正方形.
(1)求证:
;
(2)试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388c0990291dfcf9ce3060c06ddd810d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f70db67d96a5bf6d5c6b93ed64952d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb886661302d1bc974b0c4f2458fcea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693dd24614173c8295bc7cf97fd5725a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7122f2ae84bff5b73095f78cafe04f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64dafa5de92d59009eda97f12ac5d71.png)
(2)试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
5 . 已知函数
.
(1)证明:
;
(2)证明:函数
在
上有唯一零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6af8a20bc7e1d4083f5b593945f5b1d4.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eee1b2e5b22424039fc42c00bef10db.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f900c79909dbc37e24dd1cd794d2a14f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88e93310e85e58313d4ec99a2cb0553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733b49a914ddebf61fc728b0d0cf9442.png)
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名校
6 . 对于定义在
上的函数
,若存在
,使得
,则称
为
的一个不动点.设函数
,已知
为函数
的不动点.
(1)求实数
的取值范围;
(2)若
,且
对任意满足条件的
成立,求整数
的最大值.
(参考数据:
,
,
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3102c0a2f53b80f9dddbf9352537e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9395f82b00d09c3ba16e86a400172d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0111d2a71f2d27270e9335b15be7c560.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b962bb3cf61d0fd2bc73a08765012926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232d1ce3ad14256b1543e6007ff1675d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb78894fa01ddd5a4cb80a89f96e8b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b7cfcc147916ae7eeb5d557fea945e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50101047632b94dcd5cf8035b093cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/956a3e5d7b626166aea688dadf881021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a80d0cbe26bbac441eceb3e71a29010e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1597277c8cb70bc9aaed8a21fc0cbea6.png)
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7 . 已知函数
是偶函数,且
.当
时,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e81e15b871dd32b2438ef8025bcc42d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb00fdf681e3ea2f61abbe7b33a639a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac1e85463a3177f487d896b3d1d24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09917277348d02731222306d448123c7.png)
A.![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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7卷引用:安徽省合肥市2023届高三下学期第一次教学质量检测数学试题
安徽省合肥市2023届高三下学期第一次教学质量检测数学试题(已下线)专题04导数及其应用(选填题)(已下线)河北省石家庄市2023届高三质量检测(一)数学试题变式题11-16陕西省联盟学校2023届高三下学期第三次大联考理科数学试题(已下线)第九章 导数与三角函数的联袂 专题二 导数法求含三角函数的函数极值与最值 微点3 导数法求含三角函数的函数极值与最值综合训练重庆市第一中学校2023-2024学年高二上学期12月定时练习数学试题(已下线)专题23 导数及其应用小题
8 . 已知函数
,以下结论不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a49ea6bcc53bd5251cdd8ef5025bc5.png)
A.![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.![]() ![]() |
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