1 . 已知函数
.若不等式
对
恒成立,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35870334be1304cd1f170abd2358feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd94daf2b03bdc1f0561e589f2b58c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 已知
,
,若点A为函数
上的任意一点,点B为函数
上的任意一点.
(1)求A,B两点之间距离的最小值;
(2)若A,B为函数
与函数
公切线的两个切点,求证:这样的点B有且仅有两个,且满足条件的两个点B的横坐标互为倒数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331d70266454df40256268b19b055a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a49b0d7aedc593a3e87fbab7c31ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)求A,B两点之间距离的最小值;
(2)若A,B为函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
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2019-09-29更新
|
865次组卷
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3卷引用:2019年云南省师范大学附属中学高三上学期第一次月考数学(理)试题
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3 . 已知函数
.
(1)讨论函数
的单调性;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea1a650ffa47f1f85c45a13acf50c9c.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76ee2d48fe9913fbd8d957b572dc48a.png)
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2019-08-02更新
|
1397次组卷
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2卷引用:云南省昆明市2018-2019学年高二下学期期末考试数学(理)试题
4 . 已知函数
.
(Ⅰ)若曲线
在点
处的切线经过点
,求实数
的值;
(Ⅱ)求证:当
时,函数
在定义域上的极小值大于极大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057dbc4685939a1b5d906def82b62da0.png)
(Ⅰ)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅱ)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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5 . 已知函数
.
(1)若
,求
的值;
(2)已知某班共有
人,记这
人生日至少有两人相同的概率为
,
,将一年看作365天.
(i)求
的表达式;
(ii)估计
的近似值(精确到0.01).
参考数值:
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56dfc13191400ebd41dcd1750efc2699.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知某班共有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532084481ae3a67c8208b7783bf22e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb86b569914509657744de5f6834164.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532084481ae3a67c8208b7783bf22e8e.png)
(ii)估计
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66c983bfb78c8276d98ed149d2a8b809.png)
参考数值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f81270de038c48e62ff81cca69cca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5df2682b6595080a2a014da57dde06c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698eb096473313df41d5f7fdb1afafc5.png)
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6 . 已知函数
,
,
.
(1)当
时,讨论函数
的零点个数.
(2)
的最小值为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9de719dcc4468ca5b923581a63a0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae88190d80c2bc109449fe8852a4c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08390369ffbdc53a8c75c351b5750120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9de719dcc4468ca5b923581a63a0c5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3c2be7482719651bcf491949681e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07b3598ead92435898950756adb369f.png)
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2019-05-17更新
|
1780次组卷
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9卷引用:【市级联考】云南省昆明市2019届高三高考模拟(第四次统测)文科数学试题
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7 . 已知函数
.
求
的单调区间和极值;
当
时,证明:对任意的
,函数
有且只有一个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1685f4d35ae1a076ae0fb74988ec8e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69c13a09123ae873e0b0501aaecc507e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5036e26e77152eb05955d2aceca93950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2021d761480a8b3b1a8ab5da8c505cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16635273b7dfaaf3b4c86594420c6e77.png)
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8 . 设
,函数
,
(1)讨论
的单调性;
(2)若
有两个相异零点
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d827f87e10a7848797480161dcf3cc.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e3090a098e891e1883168719f7ad05.png)
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9 . 已知函数
,
.
(1)若曲线
的切线
经过点
,求
的方程;
(2)若方程
有两个不相等的实数根,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aebf798213615bbf6b7911fb0667745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e2512fa0dd8a511729929e2a69ad6e.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49756172230de326c6b84e89bcf0eae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc154a401be4ce83bc265d130365744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2018-05-14更新
|
1176次组卷
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2卷引用:【全国市级联考】云南省昆明市2018届高三5月适应性检测数学文试题
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10 . 已知函数
.
(1)
时,求函数
的单调区间;
(2)设
,使不等式
对任意的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535c2998d47ffaab2938ccf73972c392.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab90968836334c7d96630134c06df38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2e7d7e1c6b53271b6828552d3f7e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87e4d8a0497dbbeeed6139db4019f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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