名校
解题方法
1 . 若非空实数集X中存在最大元素M和最小元素m,则记
.下列命题中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63cf0f3392d77db21347ed4e94812a6.png)
A.已知![]() ![]() ![]() |
B.已知![]() ![]() ![]() ![]() |
C.已知![]() ![]() |
D.已知![]() ![]() |
您最近一年使用:0次
今日更新
|
86次组卷
|
3卷引用:上海市复旦大学附属中学2022届高三上学期9月月考数学试题
名校
解题方法
2 . 记
.
(1)若
,求
和
;
(2)若
,求证:对于任意
,都有
,且存在
,使得
.
(3)已知定义在
上
有最小值,求证“
是偶函数”的充要条件是“对于任意正实数
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d80225e12934cd8d4ffc73d5fad815d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04beea76c59a6c5b096d8c5a3b77f8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1b9f62690647a1597f4000ad5a64b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c8381377b90826897eb4bf16cb3bae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28034dcafe542a98d95d4504ad7d8a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4def7108b0a2338f07a0143b00b48271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3761d7ab4d00c91177fdbde67af36089.png)
(3)已知定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/625e9d3c298a595678933b59583632c2.png)
您最近一年使用:0次
真题
解题方法
3 . 已知函数
的定义域为R,定义集合
,在使得
的所有
中,下列成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff42ff0e772a602981c54616134a52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98d299979423e5ae74b618b07d10c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
A.存在![]() | B.存在![]() ![]() |
C.存在![]() | D.存在![]() ![]() |
您最近一年使用:0次
7日内更新
|
1198次组卷
|
4卷引用:2024年上海夏季高考数学真题(网络回忆版)
名校
4 . 设正数
不全相等,
,函数
.关于说法
①对任意
都为偶函数,
②对任意
在
上严格单调递增,
以下判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56667aabbe787eb1c3189d487d203e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d74781f2fcb2c572de65c4f702d5457.png)
①对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75c03244f2565ccad815ed9305655b4.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75c03244f2565ccad815ed9305655b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d720165be8b61db4a8b305ad47c7f2a0.png)
以下判断正确的是( )
A.①、②都正确 | B.①正确、②错误 | C.①错误、②正确 | D.①、②都错误 |
您最近一年使用:0次
解题方法
5 . 已知
是函数
有四个零点,记
的导函数为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51fb3ef65a6ee809219a3f9f78d127fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
A.![]() | B.![]() |
C.![]() ![]() ![]() | D.存在![]() ![]() |
您最近一年使用:0次
名校
解题方法
6 . 已知
为实数集
的非空子集,若存在函数
且满足如下条件:①
定义域为
时,值域为
;②对任意
,
,均有
. 则称
是集合
到集合
的一个“完美对应”.
(1)用初等函数构造区间
到区间
的一个完美对应
;
(2)求证:整数集
到有理数集
之间不存在完美对应;
(3)若
,
,且
是某区间
到区间
的一个完美对应,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4c42648f413abc4ec6b042f0924e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e7ee80da08376cb9a6f0ac641b2d1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)用初等函数构造区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f14df2d8d1fea71da4197e81b6ee3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d65bdc820ab87b9a7909d2be591abec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)求证:整数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067802ecb7978511f798ef27d02e890b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316ecb1589c3cc179e2f62507020771e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8835e96965b13d49dd1481403eb997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aff8d9b6533ff319420cdc5e8740b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e2bb6cfd4b2fa49622dc9b7c39b62b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
7 . 已知函数
是
的导函数,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9ca8d13fcffa6e9fb07efdd05e4a56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.“![]() ![]() |
B.“![]() ![]() |
C.若不等式![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
8 . 对于正整数n,
是小于或等于n的正整数中与n互质的数的数目.函数
以其首名研究者欧拉命名,称为欧拉函数,例如
(
与
互质),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7cc0ad7521b5771950aea983f0c1c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7cc0ad7521b5771950aea983f0c1c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c9e69c7d5a3d7a5633a373a8a39544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786c6406780167f9744d0f9e9682e471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
A.若n为质数,则![]() | B.数列![]() |
C.数列![]() | D.数列![]() |
您最近一年使用:0次
7日内更新
|
259次组卷
|
3卷引用:湖北省宜荆荆2024届高三下学期五月高考适应性考试数学试题
湖北省宜荆荆2024届高三下学期五月高考适应性考试数学试题 吉林省通化市梅河口市第五中学2024届高三三模数学试题(已下线)高二数学期末模拟试卷02【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)
名校
解题方法
9 . 设定义域为
的函数
在
上可导,导函数为
.若区间
及实数
满足:
对任意
成立,则称函数
为
上的“
函数”.
(1)判断
是否为
上的
函数,说明理由;
(2)若实数
满足:
为
上的
函数,求
的取值范围;
(3)已知函数
存在最大值.对于:
:对任意
与
恒成立,
:对任意正整数
都是
上的
函数,问:
是否为
的充分条件?
是否为
的必要条件?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851c68ef2e0703706f3b528daa902eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b639b31035fc3862454ff8ce2b9a5154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6c26e485c3956d1576524fbc17927f.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db76af819439f36b33fd89b7911a45cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd50020c0e3198d4a6b2d26a413b1b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f352df4a168a31caef9c4e017dae0d74.png)
(2)若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3162d2c7b650bba3e401ffbb1e13bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b34e8d8b62a1d94748c849f066406169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6c26e485c3956d1576524fbc17927f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b968a1d9d735d2482aef72fb73e9707a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58196b9e63ec00aa1119052b6de6ae12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e9f933b77561af59f821a9f7bd46b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca89e1424190793ebcd3944d73e25c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
10 . 在数字
和
中,更大的数字是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172370f9adae2e388a4a777ad92ca18f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/013407782cf6bdec227a4e6ad8c9dba7.png)
您最近一年使用:0次