名校
解题方法
1 . 已知函数
的图象在点
处的切线方程为
.
(1)则实数a的值为__________ ;
(2)设
,若
对任意的
恒成立,则k的最大整数值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9087da83d78b737d7ac90458c171d5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc568fbc1480ba87cfdc2b6b3c71200.png)
(1)则实数a的值为
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b034f42a44cb15e6b320f24dd7cdd0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd179a4430d2f13d30bda9a42248ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0aa2ef928b6e3341d0a0dc6d8055b9.png)
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真题
解题方法
2 . 设函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1c1eb55d7120d8a58c14cb5c42b96b.png)
A.当![]() ![]() |
B.当![]() ![]() ![]() |
C.存在a,b,使得![]() ![]() |
D.存在a,使得点![]() ![]() |
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今日更新
|
5500次组卷
|
5卷引用:高二数学期末模拟试卷01【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)
(已下线)高二数学期末模拟试卷01【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)(已下线)2024年高考数学真题完全解读(新高考Ⅱ卷)专题03导数及其应用(已下线)2024年新课标全国Ⅱ卷数学真题变式题11-152024年新课标全国Ⅱ卷数学真题
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3 . 已知
,若函数
有两个不同的零点,则a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a093f66705f95dc75bcb89e00ac8258.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知函数
.
(1)求函数
的单调区间;
(2)若函数
在
上有零点,且
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b56accc7f13246c9fd860a267cd66893.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d642efd3970ac70d52849baa0cd64a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b21961de32caed27d2b519e1961f68.png)
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名校
解题方法
5 . 已知函数
,且
在区间
上单调递增,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75d9579e38a3e7e2ca8d64db48ac91c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0113fd4c7d157757571f9a009e02af.png)
A.0 | B.![]() | C.![]() | D.-1 |
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2024-06-12更新
|
452次组卷
|
3卷引用:5.3.2函数的极值与最大(小)值(2)
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6 . 已知函数
,若函数
有 3 个极值点
,则实数
的取 值范围是_______ ; 若
,则实数
的取值范围是 _____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f9180806e001b88049b9441af6ad1d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcee20976de0e0e8c1ccd7a951674691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9facbec77e33a43dc5cec58eea852d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024高三·全国·专题练习
解题方法
7 . 已知函数
,若不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd3e2dbf7b4045d0e01a16d27a2d12e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debc8cbedc653426b661fc3082671c1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
8 . 给出以下三个材料:
①若函数
的导数为
,
的导数叫做
的二阶导数,记作
.类似地,二阶导数
的导数叫做
的三阶导数,记作
,三阶导数
的导数叫做
的四阶导数…,一般地,n-1阶导数的导数叫做
的n阶导数,即
,
;
②若
,定义
;③若函数
在包含
的某个开区间
上具有n阶的导数,那么对于
有
,我们将
称为函数
在点
处的n阶泰勒展开式.例如,
在点
处的n阶泰勒展开式为
.根据以上三段材料,完成下面的题目:
(1)若
,
在点
处的3阶泰勒展开式分别为
,
,求出
,
;
(2)比较(1)中
与
的大小;
(3)证明:
.
①若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def752070b9e674fdd3c7a632647ab54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def752070b9e674fdd3c7a632647ab54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f71c87ca0e7fa8ad0a24f8d5a2854ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9c55d08be2a0f694e1e948319be61c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9b92a1988f20c45e8ba3887eeb6b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/849fe9a00128b39200a5defc403fe827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083f05aeb79c34207ddc2b162b8ce49f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369f4888f6214b4472cd16e45139ec88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78bf48ae91b57fc73e6303a829446a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6d4c5149174ffd7f841718d6af7fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1eac268e854f1d13a101ec88af5afd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6d4c5149174ffd7f841718d6af7fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1eac268e854f1d13a101ec88af5afd2.png)
(2)比较(1)中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bffc9c4bf9de4d804885955aff039ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6d4c5149174ffd7f841718d6af7fb0.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f1656e376d8067d4766f1cc14e56cd.png)
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名校
解题方法
9 . 设定义在
上的函数
的导函数为
,若满足
,且
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db17c0ebab844dad112b5b2c50551a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91770acb583f05c3ead767d247be034.png)
A.![]() ![]() |
B.不等式![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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10 . 设离散型随机变量
和
的分布列分别为
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ebe32a5013a5104260716fcc740da.png)
,
.定义
,用来刻画
和
的相似程度,设
,
.
(1)若
,
,
,求
;
(2)若
,且
的分布列为
求
的最小值;
(3)对任意与
有相同可能取值的随机变量
,证明:
的值不可能为负数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3097e6975627ac7a7fc78326aa3c680d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b945ead3c11ea96273ab77482497c010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d59165a1af56c9a1a39b4836fe1314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987292d893f960a7b4915a7023fa41eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ebe32a5013a5104260716fcc740da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e7f7f4284d08f7298e6eb8640bb569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7510226e3bef2768c91e7ba164bbd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b091aa6eaac148b56e9013e17a14ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c11f6c800b8e0410674a0c6d307d26.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a18d2bd429301b5478dcd26c572266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ca76215449448e07b0ffb35f176ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c1c46297fe3d150d2bdbd6c238dae2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![]() | 0 | 1 | 2 |
![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c1c46297fe3d150d2bdbd6c238dae2.png)
(3)对任意与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c1c46297fe3d150d2bdbd6c238dae2.png)
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