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1 . 解关于
的不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6cdf229c784c4bfec961e6c52e8994a.png)
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18-19高二·全国·假期作业
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2 . 已知不等式
.
(1)当
时,解此不等式;
(2)若此不等式对一切实数
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/506d1a8e4272eed61702a6d4e2344d0f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
(2)若此不等式对一切实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2019-12-17更新
|
945次组卷
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7卷引用:福建省莆田第二十五中学2023届高三上学期月考(一)数学试题
解题方法
3 . 利用函数![](https://img.xkw.com/dksih/QBM/2015/3/26/1572036540071936/1572036545937408/STEM/69a3f08723a247a3abe2eecaa0973434.png?resizew=123)
是减函数可以求方程
的解.
由
可知原方程有唯一解
,类比上述思路可知不等式
的解集是____________ .
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572036540071936/1572036545937408/STEM/69a3f08723a247a3abe2eecaa0973434.png?resizew=123)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572036540071936/1572036545937408/STEM/d7353ddd265c4ca19111797aa17b1d21.png?resizew=51)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572036540071936/1572036545937408/STEM/f68dcd6dcdb845a6b1b2f83cd8a7fba3.png?resizew=97)
由
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572036540071936/1572036545937408/STEM/957e221c883a4b07a78bbe258e43c965.png?resizew=57)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572036540071936/1572036545937408/STEM/2ab9eb7cca634d5cb7835f4d1f13479d.png?resizew=37)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572036540071936/1572036545937408/STEM/5f36e2bcf6f1453caf3133488da2964f.png?resizew=171)
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解题方法
4 . 已知函数
.
(1)求
在
的最小值;
(2)若方程
有两个不同的解
,且
成等差数列,试探究
值的符号.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33426d6f89e2874a389b5d884fa5a4de.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf87d9d48c3de0a5e9f1a70e51a0bef.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce90064385c4633056784c1ae375a2d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546cd7c7c03fde940c6f3d4b3d423061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91421e7703d87617f50270178decd18a.png)
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2022-11-17更新
|
926次组卷
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6卷引用:福建省莆田市第二十五中学2024届高三上学期10月月考数学试题
名校
5 . 已知函数
(
为自然对数的底数).
(Ⅰ)证明:当
时,方程
在区间
上只有一个解;
(Ⅱ)设
,其中
.若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50251c26b7ec43098eea34aad86ed882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(Ⅰ)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e507eeef7cde92071577dcb0227e525e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7efeb56b59b41e0d812cbef18d41cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6 . 设函数
.
(1)当
时,求函数
的最大值;
(2)令
,其图象上存在一点
,使此处切线的斜率
,求实数
的取值范围;
(3)当
,
时,方程
有唯一实数解,求正数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554cba705b88f6e28454fe77b96464ac.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd415208c35bb0a739f8ab1e965249ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0bb809bc30d56299069557154ebe11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96fbbb9c4b0f7937c003ef2c218c02a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e7c300c2def88e87e2a8108655993c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17381b15148bde867610d12773694474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2017-12-18更新
|
368次组卷
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4卷引用:福建省莆田第九中学2018届高三上学期第二次月考(12月)数学(文)试题
名校
7 . 已知
且
,函数
,记
.
(1)求函数
的定义域
及其零点;
(2)若关于
的方程
在区间
内仅有一解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150cc0064ebcb10bab5e1f6264f3222e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62564bba9a5cfd6cec8047446686350b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff357a3334fc8eef20035365e7f7f18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ae66c5401deed7341470ca37800463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2016-12-04更新
|
613次组卷
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10卷引用:福建省莆田第九中学2018届高三上学期期中考试数学(理)试题