解题方法
1 . 已知函数
,其中
,且
为奇函数.
(1)求a的值;
(2)若
,
,
,求集合M;
(3)若函数
,讨论函数
(k为常数)的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c49e7ffda89c48e4d92cac1e2b014e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求a的值;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68072473a5106f93e3026d992859f7a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df08da2421cb4189f7614b732f015a76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3a564aec24b9b74ccb9536e2cf0aed.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef49847ec3ba85b54129f985140c290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d2218ba6c2a0d40d6f9a9b8f17d2f0.png)
您最近一年使用:0次
解题方法
2 . 已知实数
满足
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c057ea2ec9fef49befe17571794aeb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d4fcb22b9ef5b847927d6d3437e024.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
3 . 集合
由有限个实数组成,定义集合
的离距
如下:实数轴上,集合
中的每个实数
对应一个点
,实数
对应的点
与所有这些点
的距离的算术平均数记为
,称函数
的最小值为集合
的离距,记为
.例如,集合
的离距是0,集合
的离距是2.
(1)分别求出集合
的离距;
(2)求数集
的离距;
(3)已知非空数集
满足
,试写出一个关于
的大小关系的等式或不等式,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdb777c90f9cabba8d4ed34c16f4acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e51c8010a4568d7d44f261973dea420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdb777c90f9cabba8d4ed34c16f4acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39412925212a989c503e891db840609d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c6fed9c3cf2c00ba1823c3f0a05615.png)
(1)分别求出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7384a3e8b9a7ffb00bb124ba97b7c992.png)
(2)求数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22accc2928d3370f48a84cc4703a4b07.png)
(3)已知非空数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21e6c4bb62b14f8e70d8f8b1ac911bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3598ab9c4ac9a9496c5f34b9b5fda3cf.png)
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4 . 通常我们把一个以集合作为元素的集合称为族.若以集合
的子集为元素的族
,满足下列三个条件:(1)
和
在
中;(2)
中的有限个元素取交后得到的集合在
中;(3)
中的任意多个元素取并后得到的集合在
中,则称族
为集合
上的一个拓扑.已知全集
为
的非空真子集,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552911fcffb0021a8572e82bfa6648de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb584b83ae783a0ec8a9b4628b7fca3e.png)
A.族![]() ![]() |
B.族![]() ![]() |
C.族![]() ![]() |
D.若族![]() ![]() ![]() ![]() ![]() ![]() |
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名校
解题方法
5 . 对于给定的区间
,如果存在一个正的常数
,使得
都有
,且
对
恒成立,那么称函数
为
上的“
成功函数”.已知函数
,若函数
是
上的“4成功函数”,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1da2db85b44ae9ced8c09cd19593e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25083b9086a1ed3432a2fc9c1b15619f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3469292e7aea6a50ced42cddce157b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1da2db85b44ae9ced8c09cd19593e2.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/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/691e1b95237bd609dfd15759a9206bde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/768792e2684dca75cc78d46c07c25668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334919736e5ed881f691e4ca738b4ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-03-01更新
|
326次组卷
|
8卷引用:重庆市南开中学校2022-2023学年高一上学期期末数学试题
重庆市南开中学校2022-2023学年高一上学期期末数学试题江苏省射阳中学2022-2023学年高一上学期期末数学试题(已下线)高一上学期期末考试填空题压轴题50题专练-举一反三系列(已下线)第4章 指数函数、对数函数与幂函数-【优化数学】单元测试能力卷(人教B版2019)重庆市万州第二高级中学2023-2024学年高一下学期开学考试数学试题黑龙江省哈尔滨师范大学附属中学2023-2024学年高一下学期开学考试数学试卷辽宁省沈阳市第一二〇中学2023-2024学年高三上学期第一次质量监测数学试题(已下线)专题11 不等式恒成立、能成立、恰好成立问题(过关集训)
解题方法
6 . 设
的定义域为R,若
,都有
,则称函数
为“
函数”.
(1)若
在R上单调递减,证明
是“
函数”;
(2)已知函数
.
①证明
是
上的奇函数,并判断
是否为“
函数”(无需证明);
②若对任意的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8625151f40f341575c1a71992e485188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebad7d6cac2a8c2eaa6fc5682ff9b909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)若
![](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/73465a1f9aa03481295bf6bd3c6903ac.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4747903d0563a352d8ef757483543ede.png)
①证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
②若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4dc9275cade48cab4845f2c12f0998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
.若
,不等式
恒成立,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b919a59954cf503f515e45573deba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9f109b7ce6ec37e69d54ec70643c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
8 . 已知函数
,
.
(1)设
.若
恰有两个零点
、
,且
.判断函数
的奇偶性(只需给出结论,不需写证明过程),并求实数
的值;
(2)若
,
,
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c1435ac112f1a98c40725d361d20b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd055fc5fdc69045fd6d4bca7c37eab3.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1298b16851618bb8884791817a78d0a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab0fdded94776c7e330d6c21ab4860a.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/9159bc3e165a4f2ee9d67f8f5180e7bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35eac3ba2858adffcd1f8052cd795269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea7936ad4048b3fc87a81d5469ec33e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61649f88b8cbbb573713ff3fe3097d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
9 . 已知函数
,
.
(1)写出
的单调区间,并用单调性的定义证明;
(2)若
,解关于
的不等式
;
(3)证明:
恰有两个零点m,
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0676c35e842a3a86d3b752cae5ca0576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0a1faf66cdc3558d05205fd8f5187d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3484588665d34c47ac3d2ef5c7ef5f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9947fdb8b6b390de995711ef15d82e70.png)
您最近一年使用:0次
解题方法
10 . 已知函数
(
且
)为奇函数,且
.
(1)求实数m的值;
(2)若对于函数
,用
将区间
任意划分成n个小区间,若存在常数
,使得和式
对任意的划分恒成立,则称函数
为
上的有界变差函数.判断函数
是否为
上的有界变差函数?若是,求M的最小值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dabb772b37e75b8d3d5ad0fc84a745da.png)
![](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/534ffd1dd846f0ac5b8f3747d94f0501.png)
(1)求实数m的值;
(2)若对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1d60a3c7f5eae1586a8893054d44291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d3c143fefeb2d6ba72a129de446486c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f05611dfa56c61478127da674d7edf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1ed40a8f67e93401e544284ceaaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466c69619ce71732ea09466da829f2df.png)
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