解题方法
1 . 已知函数
.
(1)当
时,解不等式
;
(2)当
时,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9eb22a666dee9eb4a9a590dd6aafc7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e693d36b6395a0e28324c29c54151a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f999f9c9246a6d128807b138d9d15de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc2607d8836f265bbc1b2821391194a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 设
,
.
(1)若x,y均为锐角且
,求z的取值范围;
(2)若
且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d018fc39fe3a5feee51a08ee8c58483e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ebed1b93046c28dd4ce381df0ca441f.png)
(1)若x,y均为锐角且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3085600fba3d8ce8403ddc8b44996f88.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7204495706847fd4c8abc55e89c9a35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598caae9102ce0b49bdd2ea12189562d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eca80d80b6e1577762585b69145736b.png)
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|
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3 . 已知函数
.
的图象,并求
的解集;
(2)
,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6016b994cb131e20bb9b2b2d30e7130a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0746f6d7da0d54296692b8ede9330e19.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d794c3af7140c07ef04547cdd0be19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/025fa762ba884166c5c50008f85df334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
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4 . 已知函数
,
(1)当
时,求
在点
处的切线方程;
(2)对任意的
时,
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd16b6624bb0c0079b0a6673b71cefe.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
(2)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b531df3eb4c81b956718f4083c1c408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b91f4066869ed85dc6fc7d8f77a57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 已知函数
.
(1)若
是
上的单调递增函数,求
的取值范围;
(2)当
时,
对
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0cf2663917582f09bc11e150b3a969.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5374bfc463f980d9dab1ffda5f59885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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2024-04-10更新
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6 . 已知函数
,若对
,不等式
恒成立,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d0e2985fd01d81912ba38f822ae322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e362f2a6ffa4b767b95b121eb409a6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa04c1e1dd25c4c6326e0a02d74c11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97bb437f1b1904f3487c1df9caeac35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6b60565848b60b9c9369273e25b2bc.png)
(1)是否存在实数
使得
在区间
上恒成立,若存在,求出
的取值范围,若不存在,请说明理由;
(2)求函数
在区间
上的零点个数(
为自然对数的底数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97bb437f1b1904f3487c1df9caeac35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6b60565848b60b9c9369273e25b2bc.png)
(1)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015c1eedc3c276edc988caf75a21b4d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e297d4a627f5badcc6874dc124e21b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b4d774577b246e5c2e694f4bd6e383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
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2024-03-11更新
|
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8 . 设
.
(1)求函数
的单调区间和极值;
(2)若关于x不等式
在区间
上恒成立,求实数a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f52efa1028c78aab888cb3f4f3ecf42.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3412b3032b48a41809613f89968a7857.png)
(2)若关于x不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a3713bb22838d9432c9e484c537e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
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9 . 设函数
.
(1)求不等式
的解集;
(2)若对于任意实数
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83885a8e289d2f6d47ae4c6d65472761.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188281cc0c7af6e95c32b9bbb94ffc21.png)
(2)若对于任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df48a667cc95383f93aa733c0336f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
10 . 已知函数
.
(1)当
时,求不等式
的解集;
(2)若
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0169995a7ddcce571cdea83157ea2979.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e3b4e02955066041a5b67549295c15.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48818d31d0e9c99a6a188b9960ac1437.png)
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