名校
解题方法
1 . 已知函数
.
(1)若曲线
在点
处的切线与直线
垂直,求该切线方程;
(2)若
是
的一个极值,求满足此条件的实数
的值;
(3)若
是方程
的两个不相等的实数根,求证:
.
(注:
是
的导函数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae6f7531d12153cfc4da391e613971c.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f84134092f31767ff9f7e8200a79fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22581bc1395203df37e56ee115e14de2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e815aee0e765e618a519eb59bfba32a1.png)
(注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
名校
解题方法
2 . 已知
,下列四个结论:①
,②
,③
,④
.其中正确的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1bb486cbf98ae341a35a17e79fae7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b0e6eb011614deef2d50ceab01c8d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e0b26fa1a2c42bf24833e241ea25a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec504e75b5fe6435a94047a2f0b9443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9dd82388f903f53c58ff6d655dd7d14.png)
A.1 | B.2 | C.3 | D.4 |
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名校
3 . 已知
且
,函数
.
(1)记
为数列
的前
项和.当
时,试比较
与2024的大小,并说明理由;
(2)当
时,证明:
;
(3)当
且
时,试讨论
的零点个数.
![](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/ff69be9f14b645d71fe4547677db36de.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e65101ee1a5a3540d9359676ba6319a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c98250092857464fbe6cc0707b89ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7416befa4d79b1101a79adb8983c95a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950581caec90a28b5fa8f1e81bf21d19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7a75bcd70f6b1a6d02dbb92e964e1b.png)
(3)当
![](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/09f86f37ec8e15846bd731ab4fcdbacd.png)
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名校
解题方法
4 . 柯西中值定理是数学的基本定理之一,在高等数学中有着广泛的应用.定理内容为:设函数
,
满足①图象在
上是一条连续不断的曲线;②在
内可导;③对
,
.则
,使得
.特别的,取
,则有:
,使得
,此情形称之为拉格朗日中值定理.
(1)设函数
满足
,其导函数
在
上单调递增,判断函数
在
的单调性并证明;
(2)若
且
,不等式
恒成立,求实数
的取值范围;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.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/8ce5b83b652a50ea15c83c826d8fb52f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38593523a246f9e59688f64444e0dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a1212aca40e8dfbb97ae428c5d40a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4306fb6d5419322b4b7b9140e06e43a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38593523a246f9e59688f64444e0dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584ef8a5b63c5a2a80372865ac0cc0a0.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acaa791feb147bd1a8bf5eb4f81a0cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a4b4a9b7f0a8c3de045fe903204800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e71b49ac6c97943138bed91aab6215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d64f25e0020c3db48bb6a767afa98a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19cf16fd398ad9782cd4f5149d0c76f.png)
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名校
5 . 已知函数
,
.
(1)讨论函数
的单调性;
(2)当函数
有两个极值点
,
且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5facb7583ea00e6d8db952d80557f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b314f6ccb0a3e4fc15685d85e55bf6.png)
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名校
6 . 已知
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57352b5b5d5825cddce0d989b9af7d5b.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-05-09更新
|
1058次组卷
|
4卷引用:湖南省永州市第一中学2023-2024学年高二下学期6月月考数学试题
湖南省永州市第一中学2023-2024学年高二下学期6月月考数学试题(已下线)专题6 指数、对数同构问题【练】(高二期末压轴专项)吉林省长春市东北师范大学附属中学2024届高三下学期第五次模拟考试数学试题甘肃省兰州市西北师大附中2024届高三第五次诊断考试(三模)数学试题
名校
7 . 已知实数
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c965c7473b7044a02c9b7c91cb89394e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-05-09更新
|
598次组卷
|
6卷引用:期末押题卷02(考试范围:高考全部范围)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)
(已下线)期末押题卷02(考试范围:高考全部范围)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)吉林省长春外国语学校2023-2024学年高二下学期期中考试数学试题安徽省芜湖市安徽师范大学附属中学2023-2024学年高二下学期6月测试数学试题安徽省皖豫名校联盟&安徽卓越县中联盟2024届高三联考5月三模数学试题辽宁省鞍山市第一中学2024届高三下学期八模数学试卷福建省泉州第五中学2024届高三高考热身测试数学试题
名校
8 . 下列判断正确的是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 已知函数
(
为正实数).
(1)讨论函数
极值点的个数;
(2)若
有两个不同的极值点
.
(i)证明:
;
(ii)设
恰有三个不同的零点
.若
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4408d41d16260ea1c6c5db1af1270b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d1540b6b10f07a867618a1eec02e2a1.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d277a5747e76c386963b5c98a7c69745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a0a547c81fe36ab8c3ea79622ce7ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd3b7f705212fcf5aae1294430dc0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b70d5c2f93f5f25061330a4dd6bac35.png)
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名校
解题方法
10 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1b70d8169a0264375fb4cc7b85a011.png)
(1)若函数
与
的图象存在公切线,求
的取值范围;
(2)若方程
有两个不同的实根
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1b70d8169a0264375fb4cc7b85a011.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576469e4f51c1ede73f7f0458f504418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f03fd662f69ce3e5449c08e00b963194.png)
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