1 . 利普希兹条件是数学中一个关于函数光滑性的重要概念,设
定义在
上的函数,若对于
中任意两点
,都有
,则称
是“
-利普希兹条件函数”.
(1)判断函数
,
在
上是否为“1-利普希兹条件函数”;
(2)若函数
是“
-利普希兹条件函数”,求
的最小值;
(3)设
,若存在
,使
是“2024-利普希兹条件函数”,且关于
的方程
在
上有两个不相等实根,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f58d4591d668b4bc32fae4faab8298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2712b1acecc1d933cca91078b76ffea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44edb8cc6555fc6ec8d0bfd7d5b33f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1044dcf4fba551e1b7fbfeb895ea08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e711f9ca607fd1b077e742d1cc156bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f172b078edc129d4ad341fc2bfb13d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92538987cf225663a769b58a933ac6af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解题方法
2 . 已知函数
的定义域为
,若
,且
为偶函数,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66bc77f7320d20c9281735f21560d422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee798afc6ca1bbee1f324fc7e0abafd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3587ff064f9af01371279ab75d22116c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
3 . 已知
,
,
,
,则下列大小关系正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678bc4e3642a01f2e6c3f82ae6af82b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503a28c3b4ee6e3894b28cc0c84deec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf9fbba9a4583674e07eaf65f4f0493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce59668a3be332c863098b978da5b85.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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今日更新
|
456次组卷
|
4卷引用:海南省儋州市2023-2024学年高二下学期期末考试数学试题
4 . 已知定义在
上的偶函数
满足:当
时,
,且
对一切
恒成立,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eaeb2ab68a49074d623ffca072fed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64237298902c25796c208fbf3e8a251d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 已知定义在
上的函数
为奇函数,且函数
在区间
上单调递增,则
的解集为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b82f4b1aa4135c38f9c6933c53fab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c04742d620bd6b21229b3f39dd592a.png)
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名校
6 . 如图,某公园内有一块边长为2个单位的正方形区域
市民健身用地,为提高安全性,拟在点A处安装一个可转动的大型探照灯,其照射角
始终为
(其中
,
分别在边
,
上),则
的取值范围______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7023ec0f513c7d0ef86859a5ede54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5604d3e156df3e7ccca0ccec9c9d45.png)
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昨日更新
|
232次组卷
|
5卷引用:专题03 高一下期末考前必刷卷01(基础卷)-期末考点大串讲(人教A版2019必修第二册)
(已下线)专题03 高一下期末考前必刷卷01(基础卷)-期末考点大串讲(人教A版2019必修第二册)(已下线)专题03 平面向量的数量积常考题型归类-期末考点大串讲(人教B版2019必修第三册)安徽省合肥市第一中学2023-2024学年高一下学期5月期中联考数学试题(已下线)专题2 以平面向量数量积为背景的最值与范围问题【讲】(高一期末压轴专项)江苏省前黄高级中学2024届高三下学期三模适应性考试数学试题
解题方法
7 . 若函数
对于任意
,总存在
使得
,则称
是
上的“
阶依赖函数”.已知函数
是
上的“
阶依赖函数”,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831e78829eef3525499e87cb9f908c17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d73f13cccf2bdcdbee8a01ece94282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0949462abf53799076637580e85bd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd8466b576ad34d6ef492599940f4b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2cc4cd1e8bcb4b75b6e799156736e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 设函数
是定义在
上的奇函数,则“
在
上为严格增函数”是“
在
上的最小值为
”的( )条件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a50188f84f379b3d0418c54cbade7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32822a106d217ffdec43557a236f786.png)
A.充分非必要 | B.必要非充分 | C.充要 | D.既非充分又非必要 |
您最近一年使用:0次
名校
解题方法
9 . 对正实数
,若定义在
上的函数
满足:对任意的实数
,都有
,则称
是“
增函数”. 现给出如下两个命题:命题甲:若对一切正有理数
,函数
均为“
增函数”,则
是
上的增函数,命题乙:若对一切正无理数
,函数
均为“
增函数”,则
是
上的增函数,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4317d70f0927bad41f61019c9e2e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
A.甲是真命题,乙是假命题 | B.甲是真命题,乙是真命题 |
C.甲是假命题,乙是假命题 | D.甲是假命题,乙是真命题 |
您最近一年使用:0次
名校
10 .
,已知
是定义在
上的偶函数,且
时,
,则集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9163ebe812708ee5337d62298c2e3363.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08793fa6cbcd2da8a41618ba4065649c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986cda000d28188fbf069d4587c7e23f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb02fa6a94d9dfc5378e2b8a52a3a4a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9163ebe812708ee5337d62298c2e3363.png)
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