1 . 已知函数
.
(1)若
,求不等式
的解集;
(2)若
,证明:
有且只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2cb26c8b2ee4296797abb6a70c97fd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28041c5e5949c193468e398cf814cbdf.png)
您最近一年使用:0次
2023-07-11更新
|
340次组卷
|
5卷引用:陕西省汉中市2022-2023学年高二下学期期末理科数学试题
名校
解题方法
2 . 设
是定义域为
的函数,如果对任意的
,
均成立,则称
是“平缓函数”.
(1)若
,试判断
是否为“平缓函数”并说明理由;
(2)已知
的导函数
存在,判断下列命题的真假:若
是“平缓函数”,则
,并说明理由.
(3)若函数
是“平缓函数”,且
是以
为周期的周期函数,证明:对任意的
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec94294313030bb5554b79e8ceb407a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67e9d063f31e28b30e052bfbf7002663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e808873b814cf720131eeed83e88bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b804ef2e9a9d20629e29d1f6fbfb5b7.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec94294313030bb5554b79e8ceb407a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49a2b43fdce5aaae58c0907de23cbc6c.png)
您最近一年使用:0次
2023-11-21更新
|
417次组卷
|
6卷引用:模块三 专题2 专题1 导数运算与几何意义的应用
(已下线)模块三 专题2 专题1 导数运算与几何意义的应用(已下线)模块三专题2 专题3 导数的几何意义与运算【高二下人教B】(已下线)模块三 专题5 导数的几何意义与运算【高二下北师大版】上海市上海大学附属中学2023-2024学年高三上学期期中考试数学试卷上海市浦东新区南汇中学2024届高三上学期12月月考数学试题(已下线)湖南省长沙市雅礼中学2023-2024学年高一下学期期中考试数学试题变式题16-19
名校
3 . 设平面向量
、
的夹角为
,
.已知
,
,
.
(1)求
的解析式;
(2)若
﹐证明:不等式
在
上恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/956879af388928628970155bdb5c2737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8e69e4abd4e261077ed177c25ff74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e074c209d628251349ecb15d76dfaa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafdd5eff594c3ac6bc585b05c644fe5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bcd4e186c9b564603e00e4dfd0e8dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe58c11b71e0ce7e6263b8112aa6140c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51742bc5df0b18cd3a6ca5abfb373bcc.png)
您最近一年使用:0次
2023-06-28更新
|
405次组卷
|
3卷引用:四川省泸县第一中学2023-2024学年高二上学期开学考试数学试题
名校
4 . 给定函数
,若点
是
的两条互相垂直的切线的交点,则称点
为函数
的“正交点”.记函数
所有“正交点”所组成的集合为
.
(1)若
,判断集合
是否为空集,并说明理由;
(2)若
,证明:
的所有“正交点”在一条定直线上,并求出该直线;
(3)若
,记
图像上的所有点组成的集合为
,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a903745cd2cb536443d07579b606ece5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e38720dfaee832067188cc5e8db54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d933e743f22ff72361ee541e886603a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4815b1d16a7ae485ff0bba0b397e893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-06-25更新
|
417次组卷
|
7卷引用:上海市建平中学2022-2023学年高二下学期期末数学试题
上海市建平中学2022-2023学年高二下学期期末数学试题(已下线)模块一 专题4 《导数的概念、运算及其几何意义》B提升卷(高二人教B版)(已下线)模块一 专题5 《导数的概念、运算及其几何意义》B提升卷(高二北师大版)(已下线)期末测试卷01(测试范围:第1-8章)-备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)(已下线)专题09 导数及其应用 压轴题(六大题型)-备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)(已下线)上海市高二下学期期末真题必刷04(压轴题)--高二期末考点大串讲(沪教版2020选修)上海市南模中学2024届高三上学期期中数学试题
名校
解题方法
5 . 已知函数
,
.
(1)若对任意的
,
恒成立,求实数
的取值范围;
(2)设函数
,
在区间
上连续不断,证明:函数
有且只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b586d5da50edf2b5d624b1f3368570eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a981aa485843b0c1c197937a1400d026.png)
(1)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3accf1ec50ebf6f12a68fae563592304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5493f9035409451fccf70b7dafa3dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f77f8111c7805e673a644b0a690dcc.png)
您最近一年使用:0次
2023-06-13更新
|
480次组卷
|
4卷引用:湖南师范大学附属中学2023-2024学年高二上学期入学考试数学试题
6 . 已知函数
,
.
(1)若
是奇函数,求a的值并判断
的单调性(单调性不需证明);
(2)对任意
,总存在唯一的
,使得
成立,求正实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c064cd16c1c95023009c344564a1022a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad0bcb38bd67c085ab01b13cf7a3e05.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3715365d7cf7959b963815c32327c4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30a4750430b4b0e9daa3edbef242184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
您最近一年使用:0次
2023-06-12更新
|
1386次组卷
|
3卷引用:2023年6月浙江省学业水平适应性考试数学试题
名校
解题方法
7 . 对于函数
,若在其定义域内存在实数
、
,使得
成立,称
是“
跃点”函数,并称
是函数
的“
跃点”.
(1)求证:函数
在
上是“1跃点”函数;
(2)若函数
在
上是“1跃点”函数,求实数
的取值范围;
(3)是否同时存在实数
和正整数
使得函数
在
上有2022个“
跃点”?若存在,请求出所有符合条件的
和
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c3d9d0566b6a8f09e35479fbb584fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c39455dd7479d54bec0bfec7e4444cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8beea5150be3a27f958b6ba28edd2a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)是否同时存在实数
![](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/3aede6e541ca96009882cb172a2796b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b9f2ab6b0423d25bc6a1a490f0d919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
有两个极值点
,且
.
(1)求
的取值范围;
(2)若
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa30c3a4e1a0af2862839b6ac526a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915b3d29d0c7dd83c188e3ce31f52fc4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b331ec2c8bf52f0f6eecef1aafda27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bef9ada2c7a35775fe3dde8aead5d7.png)
您最近一年使用:0次
2023-05-28更新
|
974次组卷
|
3卷引用:重庆市第八中学校2022-2023学年高二下学期7月调研数学试题
名校
解题方法
9 . 设函数
,其中a为常数.对于给定的一组有序实数
,若对任意
、
,都有
,则称
为
的“和谐数组”.
(1)若
,判断数组
是否为
的“和谐数组”,并说明理由;
(2)若
,求函数
的极值点;
(3)证明:若
为
的“和谐数组”,则对任意
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8beb896a3c01154585e0ec979934f602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911f2e62e650373b98e1b76fb8a8b24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33890c6b0bf167514d44139d9dca0154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774ac39e474f9c5f4e17a4c0416413cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911f2e62e650373b98e1b76fb8a8b24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b6a9ffffc0c461881b427c543924cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e7c12bff76b3a3151dc3e392c60d53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911f2e62e650373b98e1b76fb8a8b24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af0614daffb549e1adc7c24a5bbdf42.png)
您最近一年使用:0次
2023-05-11更新
|
733次组卷
|
5卷引用:上海市金山中学2022-2023学年高二下学期期末数学试题
上海市金山中学2022-2023学年高二下学期期末数学试题(已下线)上海市高二数学下学期期末模拟试卷02--高二期末考点大串讲(沪教版2020选修)上海市七宝中学2023届高三下学期4月月考数学试题上海市南洋中学2023届高三三模数学试题上海市静安区风华中学2024届高三上学期10月月考数学试题
名校
解题方法
10 . 已知函数
.
(1)若
,求证:函数
的图象关于点
中心对称;
(2)若
,且关于
的不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8df2dd829c8d0b369e6ce0752f96fe.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fefeac0d38a1a529666ebbb9278835a2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558e11d700481dc414d5d073b4b88a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda3fef556938fce034a3a7a706fc71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-11-14更新
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816次组卷
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3卷引用:安徽A10联盟2021级高二上学期开学摸底数学试题(北师大版)