名校
解题方法
1 . 已知函数
,
.
(1)若
,试判断函数
的奇偶性,并用奇偶性定义证明你的结论;
(2)当
时,求不等式
的解集;
(3)若存在
使关于x的方程
有四个不同的实根,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72bc09352dfb8a9a9df6d97a7a49beb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c93d770f34594693cba4e160fc4687d.png)
您最近一年使用:0次
名校
2 . 已知函数
且
.
(1)判断函数
的奇偶性,并证明;
(2)若
,证明函数
在区间
上单调递减;
(3)是否存在实数
,使得
的定义域为
时,值域为
,若存在,求出实数
的取值范围;若不存在,则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85e60be9b6817c1401cbd33d361dbd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466c3c575b0420a2d8a5843579059769.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320cba4d29e050a7e9f4e3b24bdbbc86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f5ce6cbcf094a780156547c4ce695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
3 . 已知函数
各项均不相等的数列
满足
.令
.给出下列三个命题:(1)存在不少于3项的数列
使得
;(2)若数列
的通项公式为
,则
对
恒成立;(3)若数列
是等差数列,则
对
恒成立,其中真命题的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e115dd0cb0c28b33cdc1a43e9be779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6044fe76e20b5da7861f3d9b3f3143e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec26010780db181e89a51f780743f6ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d87a9b5258b1a5eaee3b71004a4838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8fcccbb1234ad67314c96f9856e240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1a21f360eab1fb27b8cc15db4c04a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da6273df1952961f128bb340bc28e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2cc49cadf5bf94f8df8318fa7bd519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
A.(1)(2) | B.(1)(3) | C.(2)(3) | D.(1)(2)(3) |
您最近一年使用:0次
2020-11-15更新
|
1711次组卷
|
6卷引用:数学-6月大数据精选模拟卷04(上海卷)(满分冲刺篇)
(已下线)数学-6月大数据精选模拟卷04(上海卷)(满分冲刺篇)上海市南洋模范中学2021届高三上学期期中数学试题2019年上海市上海师范大学附属中学高三下学期第二次质量检测数学试题(已下线)考向03 函数及其性质-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)考向15 等比数列-备战2022年高考数学一轮复习考点微专题(上海专用)上海交通大学附属中学2021-2022学年高一下学期5月线上月考数学试题
名校
4 . 设对集合
上的任意两相异实数
,
,若
恒成立,则称
在
上优于
;若
恒成立,则称
在
上严格优于
.
(1)设
在
上优于
,且
是偶函数,判断并证明
的奇偶性;
(2)若
在
上严格优于
,
,若
是
上的增函数,求证:
在
上也是增函数;
(3)设函数
,
,若
,是否存在实数
使得
在
上优于
,若存在,求实数
的最大值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/7ec6c7a1da7ecaef51a3d08fbcdf2821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e938b003ed30316afc6163e1f856c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7863b54185da5a3f1a765e1aa0577e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7863b54185da5a3f1a765e1aa0577e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdfccbef2633579898f3ea42b1270c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429b0da1fc8d6d13f325a52c30402c54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a6b5c15ccfc9cb76a3cdf6f0d6d946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da4e996e7571b2e9bc2d094dc502210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2020-09-06更新
|
1062次组卷
|
4卷引用:上海市建平中学2020届高三下学期3月月考数学试题
5 . 若函数
的图像上存在两个不同的点关于
轴对称,则称函数
图像上存在一对“偶点”.
(1)写出函数
图像上一对“偶点”的坐标;(不需写出过程)
(2)证明:函数
图像上有且只有一对“偶点”;
(3)若函数
图像上有且只有一对“偶点”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146d28ee1cc1dab15ee114ccfd0ae820.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11095a17ed8667ddab91a021eaf4830a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
6 . 已知函数f(x)
(cosθ+1)cos2x+cosθ(cosx+1),有下述四个结论:①f(x)是偶函数;②f(x)在(
,
)上单调递减;③当θ∈[
,
]时,有|f(x)|
;④当θ∈[
,
]时,有|f'(x)|
;其中所有真命题的编号是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b199d124fb9a5bc8438c9884f04534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe6e1109a54d68b26472344efa9e5cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b199d124fb9a5bc8438c9884f04534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61dc1a1aff0664b6a68f6ff68aa1406a.png)
A.①③ | B.②④ | C.①③④ | D.①④ |
您最近一年使用:0次
名校
7 . 已知
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa16219c81e59619944814961f4f0c8.png)
(1)讨论
的奇偶性;
(2)当
为奇函数时,若方程
在
时有实根,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa16219c81e59619944814961f4f0c8.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6dffb2d7203d3d40dae17b25b739c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2019-01-31更新
|
944次组卷
|
3卷引用:山西省朔州市怀仁市重点中学2019-2020学年高一上学期期末数学试题