名校
1 . 对于函数
, 若存在
,使得
,则称
为函数
的 “不动点”;若存在
,使得
,则称
为函数
的“稳定点”.记函数
的“不动点”和“稳定点”的集合分别为A和B,即![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732c1cd5c72ed679ddcb0e3b1e08138d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a087d67f13276fbef8eaa8e82718dc8.png)
(1)设函数
,求A和B;
(2)请探究集合A和B的关系,并证明你的结论;
(3)若
,且
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea844642720c083f09f158f56dabccd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b359345c5afa1739bf5ebf8982e1d959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b359345c5afa1739bf5ebf8982e1d959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374054f44b9a52668f91ac7601e63c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732c1cd5c72ed679ddcb0e3b1e08138d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a087d67f13276fbef8eaa8e82718dc8.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c07bd1bced5e02c11b99392f9526f7d.png)
(2)请探究集合A和B的关系,并证明你的结论;
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afafcdd19ed39cf1c3682bfea3825b34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d02e5de0c92487382f4b98376e9740.png)
您最近一年使用:0次
2022-11-16更新
|
995次组卷
|
5卷引用:山东省潍坊市2022-2023学年高一上学期期中考试数学试题
名校
2 . 已知函数
.
(1)当
时,对任意的
,令
,求
关于
的函数解析式,并写出
的取值范围;
(2)若关于x的方程
有3个不同的根,求n的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7377b0ccd2e4c7a69919758edfc40ef.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8beee95c6754ae92beb5b5765599744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec18b3959c5e7d6cf9c79064e285ff15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd689fbacfbe6c1bd0953521bbf3638b.png)
您最近一年使用:0次
2022-11-08更新
|
1873次组卷
|
9卷引用:四川省成都市第七中学2022-2023学年高一上学期期中数学试题
四川省成都市第七中学2022-2023学年高一上学期期中数学试题广东省深圳市宝安区2022-2023学年高一上学期期末数学试题第4章 指数概念与对数函数(基础、典型、易错、新文化、压轴)专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)(已下线)第13讲函数的应用(二)(5大考点)(1)(已下线)专题4.9 指数函数与对数函数全章综合测试卷(提高篇)-举一反三系列(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】(人教A版2019必修第一册)浙江省湖州市长兴县雉城中学2023-2024学年高一上学期期末数学复习卷一湖南省永州市祁阳市第一中学2023-2024学年高一上学期第一次段考数学试题(已下线)第二篇 函数与导数专题5 切比雪夫、帕德逼近 微点4 切比雪夫逼近与帕德逼近综合训练
名校
3 . 设集合
中至少有两个元素,且S,T满足:
①对于任意
,若
,都有
;
②对于任意
,若
,则
.
(1)分别对
和
,求出对应的
;
(2)如果当S中恰有三个元素时,
中恰有4个元素,证明:S中最小的元素是1;
(3)如果S恰有4个元素,求
的元素个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61fa126ff595fe6c0b42a31148d6fd65.png)
①对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36aecba41f6f5ff0d46a29dccaaf01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11a069688e4c797fcf527eab15afa82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8339eab9c659e50db86828b65f825e22.png)
②对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566d386cbedb1c8750f4837633c2af64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a5abe56c019ac914e1fcde1865a747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5718e9c8baa106b447f9fae23e730de.png)
(1)分别对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1014d847a76d84feaa69d22f6c27e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a47661e8894db3bc283922eaf4bfa711.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af500a4e28d6f5b38390b7642eb96ed5.png)
(2)如果当S中恰有三个元素时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af500a4e28d6f5b38390b7642eb96ed5.png)
(3)如果S恰有4个元素,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af500a4e28d6f5b38390b7642eb96ed5.png)
您最近一年使用:0次
2022-11-07更新
|
614次组卷
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3卷引用:高一上学期第一次月考解答题压轴题50题专练-举一反三系列
名校
4 . 对于集合
,定义
,设
.
(1)设
,
,求
,
;
(2)若
是S的子集且
,求满足条件的
的个数;
(3)设
是正整数,若对S的任意一个
元子集
,都有
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae176533a8607eb2ebc48bc767529e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/516ca1c6590a671862a47f5bb2fd8fb4.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0705f5c8d67b4947455fc01be02b8a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cbc3a23934d36bd7f24ea81e8dadc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216c01a450f47b6ea550d8f54d4861d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a829cbbae2030c4e05d22cfadc31073.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0c0989448ea6be3ddc96587ea03124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)设
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab293d534f3615cc02a192fa3bd7f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
5 . 对正整数
,记
,
.
(1)用列举法表示集合
;
(2)求集合
中元素的个数;
(3)若集合A中任意两个元素之和都不是整数的平方,则称A为“稀疏集”.已知集合
能分成两个不相交的稀疏集的并集,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a1b26aa2a8eae39c45ab0b5e4b0888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d7155d7bd00e29d2e9324a8845735b.png)
(1)用列举法表示集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
(2)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb82d62ae6889a177c70d3adf8a91056.png)
(3)若集合A中任意两个元素之和都不是整数的平方,则称A为“稀疏集”.已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
解题方法
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
,
(1)设
,解关于
的不等式
;
(2)当
时,求函数
的最大值;
(3)若对任意的
,都有
恒成立,求正实数
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3537fd5a8075d79abefb13c21a5243e3.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c67ddd60c47e91783929c8bdf8ba8.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4f0bac314c6e6d01a4cf024da3b0f9.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca66412bfd2bd11caa6af63786278a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a8a872259fa4d5801d2ff110314944.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
7 . 已知集合
(
)具有性质P:对任意的
(
),
与
两数中至少有一个属于A.
(1)分别判断数集
与
是否具有性质P,并说明理由;
(2)证明:
,且
;
(3)当n=5时,若
,求集合A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657becc77ba5ea1f2f83dac2db8f5d51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcf01e3d8479c75e2c48037509a32b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460eeeb21bb7aee40a910f6c90b85e92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b5de1e43419f74ef5a46c509ac44f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a21adcc8de899f08f68ab04b704acc2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1d26a5065efbd0900540557f06e5a6.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d3502efe17d2c399d3ef319c81b1a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963e992724b7092e28d185967d16560c.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7970494edfaba8f53f570c0ebc6cc1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84429aff3a96fd3ec544cad66d4bf29c.png)
(3)当n=5时,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f83381978ab0c8f4714bab33c875dd.png)
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2022-10-15更新
|
384次组卷
|
2卷引用:河北省行唐启明中学2022-2023学年高一上学期10月月考数学试题
名校
8 . 已知集合
为非空数集,
,
.
(1)若集合
,直接写出集合
及
;
(2)若集合
,
,且
,求证:
;
(3)若集合
,且
,求集合A中元素的个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb8cfc6508960e8d9df86e4fb1c1481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0b31a3a2f0e3d81036338bc74c0bd6.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265e81e52218232e16c78f57b3aa0de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b26ea9b3e6e286874c5dca1badea723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e16289945d1d1c529fb1bfd4d828f413.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7591668ec1bc5e8b1f2c4dba4835d1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9473a5974fa9c4286f90f6a3637411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9225d8d0500a80b6da822005d6bb68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4d331fa6921e8ebc0b1fc4affd22ba.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
,
,其中
.
(1)若
,
,求
的单调区间;
(2)对于给定的实数
,若函数
存在最大值
,
(i)求证:
;
(ii)求实数
的取值范围(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d1c8c32d235a5f8990ac3a97907f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966d9dd819cba29980da3700422c2497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780cdda28aa7225f23abf84ae1b15c71.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对于给定的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e49d02692fe73b2d6c28a9567e568b6.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a380067a20c25338eb0312e8df6c2760.png)
(ii)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-09-29更新
|
2088次组卷
|
6卷引用:浙江省杭州高级中学钱江校区2021-2022学年高一上学期期末数学试题
浙江省杭州高级中学钱江校区2021-2022学年高一上学期期末数学试题(已下线)高一上学期期中考试解答题压轴题50题专练-举一反三系列(已下线)专题07 函数恒成立等综合大题归类(已下线)第三章 函数的概念与性质单元测试基础卷-人教A版(2019)必修第一册江苏省苏州市工业园区星海实验高级中学2023-2024学年高一上学期期末复习数学试题(已下线)第二篇 函数与导数专题5 切比雪夫、帕德逼近 微点4 切比雪夫逼近与帕德逼近综合训练
10 . 若集合
,其中
为非空集合,
,则称集合
为集合A的一个n划分.
(1)写出集合
的所有不同的2划分;
(2)设
为有理数集Q的一个2划分,且满足对任意
,任意
,都有
.则下列四种情况哪些可能成立,哪些不可能成立?可能成立的情况请举出一个例子,不能成立的情况请说明理由;
①
中的元素存在最大值,
中的元素不存在最小值;
②
中的元素不存在最大值,
中的元素存在最小值;
③
中的元素不存在最大值,
中的元素不存在最小值;
④
中的元素存在最大值,
中的元素存在最小值.
(3)设集合
,对于集合A的任意一个3划分
,证明:存在
,存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e887bc41e7c72b69482b7cb153b9f40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c7bb3662baf8ab4da46099adc0180a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16c5b1cefd28f020a899803181867be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a111d44296a6d4c373e33e0267baeb8.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbefb4190e6d31cf43ce5258ebf325c3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b064529d4274a25ea70cec901689595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c303b55101c9d049947443d85bd3d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b31852ebf26c81693dc084facc76a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a5abe56c019ac914e1fcde1865a747.png)
①
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
(3)设集合
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6卷引用:北京市朝阳区2021-2022学年高一下学期期末质量检测数学试题
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