1 . 已知函数
.
(1)讨论函数
的单调性;
(2)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abb9d33b6c7caaab000e44b5e104f55.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afaaa2eb5e2220b3cbea3cd3ae8d2329.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455c6771b68eaf5c2549f992c3aaeee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63aec2c89bf4b18a7ea1a4d55dc66640.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
,
.
(1)若函数
在
上单调递增,求实数
的取值范围;
(2)用
表示
,
中的最大值,设函数
,
,试讨论
的图象与
轴的交点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd43bf38bf6c3fa4bc5b8ffb746fcb63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbfc6f997f5465c88d68dde7fd874fe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f98aab692b27cfc120481faa6525474d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7225c625819b7bfeb393a377ec2d74a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2024-01-17更新
|
492次组卷
|
2卷引用:重庆市第八中学校2023-2024学年高一上学期期末考试数学试题
名校
解题方法
3 . 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)
您最近一年使用:0次
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)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)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(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)
名校
解题方法
4 . 已知函数
,将
的所有极值点按照由小到大的顺序排列,得到数列
,对于正整数n,则下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe71580fe0a6129ae696dd23cf32a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-02-19更新
|
5096次组卷
|
11卷引用:重庆市长寿中学2022-2023学年高三下学期3月月考数学试题
重庆市长寿中学2022-2023学年高三下学期3月月考数学试题广东省广州市执信中学2022-2023学年高二下学期期末数学试题湖北省武汉市2023届高三下学期二月调研数学试题福建省厦门双十中学2023届高三高考适应性考试数学试题广东省佛山市南海区石门中学2022-2023学年高二下学期第一次质量检测数学试题(已下线)模块六 专题3 易错题目重组卷(湖北卷)广东实验中学2024届高三上学期第一次阶段考试数学试题(已下线)第九章 导数与三角函数的联袂 专题四 利用导数证明含三角函数的不等式 微点4 利用导数证明含三角函数的不等式综合训练(已下线)广东实验中学2024届高三上学期第一次阶段考试数学试题变式题11-14(已下线)函数的应用(已下线)专题23 导数及其应用小题
名校
5 . 函数
,若关于
的方程
恰好有8个不同的实数根,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092ea166f4d9dd413423bdbf18c5f0c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd910e8af089632e20f4fa350a864157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-01-10更新
|
1264次组卷
|
4卷引用:重庆市永川北山中学校2023届高三上学期期末数学试题
名校
解题方法
6 . 对于两个函数:
和
,
的最大值为M,若存在最小的正整数k,使得
恒成立,则称
是
的“k阶上界函数”.
(1)若
,
是
的“k阶上界函数”.求k的值;
(2)已知
,设
,
,
.
(i)求
的最小值和最大值;
(ii)求证:
是
的“2阶上界函数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6afd1b3aeae1bd415dba90e50c001c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffea0f7bb26c02be91008a3a992a27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5289677c3bf66194c475c4c44f4a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06f45220c23094a3d9ef53b54b89d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2bc8d66faac1a06acfec68e28086bf.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b89d55ca6a541bce15e141a7e38285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f0ca536621ec8db02707ba65917029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ff2689759a35f3a8030b02be7a22c3.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e49794721f5504dd828acf49be37ff42.png)
您最近一年使用:0次
2022-01-24更新
|
1603次组卷
|
2卷引用:重庆市巴蜀中学2021-2022学年高一上学期期末数学试题
名校
7 . 已知定义在
的奇函数
满足:①
;②对任意
均有
;③对任意
,均有
.
(1)求
的值;
(2)利用定义法证明
在
上单调递减;
(3)若对任意
,恒有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528597e52afcd661e2aaca97e709ca29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ed85d47b4f488a9b5e211938cc5424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0aa2ef928b6e3341d0a0dc6d8055b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28f616b1f56991ee75caae3ac35208b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d8f51aac18216cabd2b0082dca6090.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
(2)利用定义法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a7a4a037a4dfe973f1eb683d93d799.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf97da45123318474a22828c99d45d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4864f1ffd5317f2f89c90ffc91ece407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2020-01-30更新
|
1913次组卷
|
2卷引用:重庆市第一中学2019-2020学年高一上学期期末数学试题
名校
解题方法
8 . 已知函数
,
.
(1)解不等式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f023d16c7a30102cb0ae856d60ecc2cd.png)
(2)是否存在实数t,使得不等式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ef8f27cee6b91bfd88aad89d65d80d.png)
,对任意的
及任意锐角
都成立,若存在,求出t的取值范围:若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7c4adef3485e8ac6e50d1926365327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/541ca543427de0dafb2c1a1254f277d3.png)
(1)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f023d16c7a30102cb0ae856d60ecc2cd.png)
(2)是否存在实数t,使得不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ef8f27cee6b91bfd88aad89d65d80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0a4fc0411071f8d419c4d922508c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc0efa8f8b017d2fb478316cef35de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2020-02-25更新
|
1021次组卷
|
3卷引用:重庆市第一中学校2018-2019学年高一上学期期末数学试题
名校
9 . 设两实数
不相等且均不为
.若函数
在
时,函数值
的取值区间恰为
,就称区间
为
的一个“倒域区间”.已知函数
.
(1)求函数
在
内的“倒域区间”;
(2)若函数
在定义域
内所有“倒域区间”的图象作为函数
的图象,是否存在实数
,使得
与
恰好有2个公共点?若存在,求出
的取值范围:若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e207cf62e3a7e282eac4c4a3455bbf9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d8f242c69dfbcdf4320422b490367cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d4522656e326cc97f8633393caf3c8.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fa487d0a0d58ffeae69ccb102c5343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2019-12-05更新
|
1203次组卷
|
3卷引用:重庆市第八中学2018-2019学年高一上学期期末数学试题
名校
解题方法
10 . 对于函数
,
与常数
,若存在
使得
成立,则称函数
与
是“
靠近函数”.
(1)设函数
,
,判断
与
是否为“1靠近函数”,并说明理由;
(2)若函数
与
为“1靠近函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea10ff765f87d9379cf875e8d425df23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e29815099a20aefdf055c71a347dbb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2f0102d111a1e63ec471da49dbd50a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90ba0d6fefae76fcdd43507c4b07b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4bba0decfa88c92d9fd153aa2b84388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-02-14更新
|
1350次组卷
|
2卷引用:重庆市南开中学2017-2018学年高一上学期期末数学试题