名校
1 . 设函数
.
(1)当
时,若直线
是曲线
的切线,求
的值;
(2)若函数
在区间
上严格增,求
的取值范围;
(3)若
且满足
,对任意的
,恒有
,求证:对任意的
,当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e99b2155565e0832a2bc405cd29843.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a9b769d70cb6f29e965c800921c8ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e54c5da8061411e6659614a6511a30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca83d5dea2d5c02ac18a9c9496ca57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1313a22f7070883f17d39700f383b504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe276c0522839b1d37086d92612aa7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc3d1fe6dd2ff21f192e14fd85062fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8deeaabea77488158d0a98639e02ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af041a320a49a5db1828a26c0613ec89.png)
您最近一年使用:0次
2022-12-02更新
|
527次组卷
|
2卷引用:上海市大同中学2021-2022学年高二下学期期末数学试题
名校
解题方法
2 . 已知实数a、b使得不等式|ax2+bx+a|≤x对任意x∈[1,2]都成立,在平面直角坐标系xOy中,点(a,b)形成的区域记为Ω.若圆x2+y2=r2上的任一点都在Ω中,则r的最大值为_____ .
您最近一年使用:0次
2021-05-11更新
|
824次组卷
|
6卷引用:模块02 不等式-2022年高考数学一轮复习小题多维练(上海专用)
(已下线)模块02 不等式-2022年高考数学一轮复习小题多维练(上海专用)(已下线)考向25 直线与方程-备战2022年高考数学一轮复习考点微专题(上海专用)上海市上海师范大学附属中学2021-2022学年高二下学期期末数学试题上海市徐汇区2021届高三二模数学试题(已下线)热点04 求函数的最值-2022年高考数学核心热点突破(全国通用版)【学科网名师堂】(已下线)专题09 平面几何与向量-备战2022年高考数学(文)母题题源解密(全国乙卷)
2022·上海·模拟预测
名校
解题方法
3 . 已知
为奇函数,当
时,
,且
关于直线
对称,设
的正数解依次为
、
、
、
、
、
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1245c7633f46a29d5dd9269b77e8487.png)
________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac1e85463a3177f487d896b3d1d24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26af862ac8e4e2fe03204b0463a7a789.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1245c7633f46a29d5dd9269b77e8487.png)
您最近一年使用:0次
2022-01-14更新
|
514次组卷
|
4卷引用:上海市2022届春季高考数学试题
名校
4 . 定义域为
的函数
,对于给定的非空集合
,
,若对于
中的任意元素
,都有
成立,则称函数
是“集合
上的
函数”.
(1)给定集合
,函数
是“集合
上的
函数”,求证:函数
是周期函数;
(2)给定集合
,
,若函数
是“集合
上的
函数”,求实数
、
、
所满足的条件;
(3)给定集合
,函数
是集合
上的
函数,求证:“
是周期函数”的充要条件是“
是常值函数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc487556ec9fca7872e6fdbbe16136d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff5f184ffc037cb5dabfd32a03a6ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875be7d4b5aee30eea8c4ad8d862914a.png)
(1)给定集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265e81e52218232e16c78f57b3aa0de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875be7d4b5aee30eea8c4ad8d862914a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)给定集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f1431bca7e0baac283abc1974afe4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3dea43b478cd72cb419548c21fad67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875be7d4b5aee30eea8c4ad8d862914a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)给定集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080550853fb08fc020f092e2e9b44843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875be7d4b5aee30eea8c4ad8d862914a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
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名校
解题方法
5 . 已知函数
.
(1)求证:函数
是
上的减函数;
(2)已知函数
的图像存在对称中心
的充要条件是
的图像关于原点中心对称,判断函数
的图像是否存在对称中心,若存在,求出该对称中心的坐标,若不存在,说明理由;
(3)若对任意
,都存在
及实数
,使得
,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4077e55784510b6adc6a040daa85eb18.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c86212cfe7338ae7adca7d58eca15fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b3ed9c4fa3bce5d45202695bbc179d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55e9f87ebd16be23db0e9fea26da11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e9fc70929247a1cdc2e8fc5c83df2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2021-12-20更新
|
727次组卷
|
4卷引用:上海市长宁区2022届高三上学期一模数学试题
名校
6 . 记
,其中
,已知
是函数
的极值点.
(1)求实数a的值;
(2)
的表达式展开可以得到
,求
的值.
(3)设函数
定义域为R,且函数
和函数
都是偶函数,若
,求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b901acae2a5949cd177ad339ca96fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)求实数a的值;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ff6618568a91b92363ec35ecb8409f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7bb64e401243a01e88407b376b9d24.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9e6cc181a815a1a1e9b7e4bb9a65490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d02059613da3797ae406925b6ee5b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae66ea2971f759345e18b65570b0e009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb553fdd94fc9bed87022f72d97d6880.png)
您最近一年使用:0次
22-23高三上·上海浦东新·开学考试
名校
7 . 对开区间
,定义
,当实数集合
为
段(
为正整数)互不相交的开区间
的并集时,定义
,若对任意上述形式的
的子集
,总存在
,使得
,其中
,则
的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095747cd995cc4524071c66ab76e5fe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fa78977d3830bb863c4df4ba362064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/b53f84ec1c2416ead2a3f92d05af188a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ca25c7ef458ef1da40d7f1d2d99c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a7792efd7f82bfa7549db4cb6ca761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232d1ce3ad14256b1543e6007ff1675d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8a593f20de490729bc067552e62661e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8145182f289fbed90bbce4fe773205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
22-23高三上·上海浦东新·阶段练习
名校
8 . 已知定义在集合上的函数
满足
,记
的最小值为
,最大值为
,则下列命题正确的是( )注:
表示集合
中元素的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99bf98ff73200c1b8baca41ef0f5c0df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17432fcc09b84a9930df7504f67ecf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8279d9dd0b7750953cb9e2098b3b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
您最近一年使用:0次
解题方法
9 . 已知函数
满足:对任意
,都有
.
命题
:若
是增函数,则
不是减函数;
命题
:若
有最大值和最小值,则
也有最大值和最小值.
则下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7389d52e6aad9c9c0fb7d9b820bdb86c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d200a7afe1e011713e14886a6887e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec6c7a1da7ecaef51a3d08fbcdf2821.png)
命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b7c2420c387be8882df4359ac10b86.png)
命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
则下列判断正确的是( )
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2021-05-14更新
|
740次组卷
|
8卷引用:模块02 不等式-2022年高考数学一轮复习小题多维练(上海专用)
(已下线)模块02 不等式-2022年高考数学一轮复习小题多维练(上海专用)上海市嘉定区第二中学2022届高三下学期开学考试数学试题上海市长宁区2021届高三二模数学试题(已下线)专题3.2 函数的单调性与最值(练)- 2022年高考数学一轮复习讲练测(新教材新高考)北京市THUSSAT2022-2023学年高二上学期9月诊断性测试数学(B)试题(已下线)专题03 函数的概念与性质(模拟练)-21号卷·A10联盟2022届全国高考第一轮总复习试卷数学(文科)试题(二)(已下线)5.3 函数的单调性(2)-2021-2022学年高一数学上册同步培优训练系列(苏教版2019)
名校
10 . 观察数列:①
;②正整数依次被4除所得余数构成的数列
;③
.
(1)对以上这些数列所共有的周期特征,请你类比周期函数的定义,为这类数列下一个周期数列的定义:对于数列
,如果________________,对于一切正整数
都满足___________________成立,则称数列
是以
为周期的周期数列;
(2)若数列
满足
,
为
的前
项和,且
,求数列
的周期,并求
;
(3)若数列
的首项,
,且
,判断数列
是否为周期数列,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d9f608508a65794125b39e67b98eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6d15b3f5b6f23a9cb341ff3e43f215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078205bbd0d854b6aaf5aa6e0a772723.png)
(1)对以上这些数列所共有的周期特征,请你类比周期函数的定义,为这类数列下一个周期数列的定义:对于数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff13e48f70a467d750be8179c63f534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6492a4d97fd8f988963cf177ec14fcb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbf62141da783d700923fa2d17b9ae0.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f61c2e3ee306d0c805f54f83761f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa9cef966e838bf77be9b00d410741c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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