名校
1 . 已知函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e06c3168a8206fa6a62e05e3d61eb3c.png)
A.存在实数![]() ![]() |
B.存在实数![]() ![]() |
C.存在实数![]() ![]() |
D.存在实数![]() ![]() |
您最近一年使用:0次
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解题方法
2 . 定义:函数
满足对于任意不同的
,都有
,则称
为
上的“
类函数”.
(1)若
,判断
是否为
上的“2类函数”;
(2)若
为
上的“3类函数”,求实数a的取值范围;
(3)若
为
上的“2类函数”,且
,证明:
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d6fe21d6ed78bfc1d2b9cc41a766c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2a699f43d6836c18eaced5758a37a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6ece875296333d786d8a671b2749255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2ec965488c7e1cea085463c7731285.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93ed0f3a123e0e3b1c08db887fa1697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47e734b17201fe992be7775714e9558.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2db4bd08a64c7ceefac83e2fce50b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673207f6b77b8192d25463d071737b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea6e1bfbda5c4f6421ed18e802aba04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1ab2e5e3dd3a1c768a88eb182b44d9.png)
您最近一年使用:0次
2024-06-04更新
|
364次组卷
|
2卷引用:山东省滨州市2024届高三下学期二模数学试题
名校
解题方法
3 . 若函数
在
上有定义,且对于任意不同的
,都有
,则称
为
上的“
类函数”.
(1)若
,判断
是否为
上的“2类函数”;
(2)若
,为
上的“2类函数”,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f0e1ac411fd3a260a5c71df178bd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62f64bce0222f01a519ab1b26236bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee4613910bb8aa030db2fc5d2768e533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f248318141e0016d38f9f5a692797f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a3616e4a7268ef41b750fe22afbcd74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f248318141e0016d38f9f5a692797f.png)
您最近一年使用:0次
2024-05-08更新
|
236次组卷
|
3卷引用:山东省德州市第一中学2023-2024学年高二下学期期中检测数学试卷
名校
解题方法
4 . 已知函数
有两个不同的极值点
.
(1)求
的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bad248263e288527d2974a80855906e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609b041d6bab322474ac57d9f1e91660.png)
您最近一年使用:0次
2024-04-07更新
|
355次组卷
|
3卷引用:山东省大联考2023-2024学年高二下学期3月质量检测联合调考数学试题
5 . 已知函数
及其导函数
满足
,且
.
(1)求
的解析式,并比较
,
,
的大小;
(2)试讨论函数
在区间
上的零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee97d8c31054a7150199058bc7b45cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a53de2e60c85b2044ed87efc5b76b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd31560d1ff739f03666ce818500e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab30faa78cc53c104f61b1cd906c365.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d331c2ced600e822884ad16bb13c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9471096d0a3ab27dcc8dec3311ec0234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e63ecfc3c4165229e5538bd3d5d6d44.png)
(2)试讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882ea00f2413de1020f2368786c6dbd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
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6 . 帕德近似是法国数学家亨利.帕德发明的用有理多项式近似特定函数的方法.给定两个正整数m,n,函数
在
处的
阶帕德近似定义为:
,且满足:
,
,
,…,
.(注:
,
,
,
,…;
为
的导数)已知
在
处的
阶帕德近似为
.
(1)求实数a,b的值;
(2)比较
与
的大小;
(3)若
在
上存在极值,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab984fa2801f780e08903b339c9d041f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8ef6c18c8edf9f4c781376d5ce400a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6b902edcff913a34589487e17c9fe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c59886eb50089cc9bee3afa10282fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089b65749e52fc6346eab9bb5c49e5b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f961273efaf91399f85f36202d5f5879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6aa31a390d3e1dc7855bc3e09ec5867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a66abbb081257b612880b4a5241b73a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8fbc7623b9264d45a0ec4b440aef7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd370c3b127fbdb77b6e5c40318328d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2db1e56c92e2ebdc5d2cae336a01b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e96546b3259afe4add331673fb835c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40765d09390381658d5b4dc0160366cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d128f7851b7771f95bffbdbf3ced02.png)
(1)求实数a,b的值;
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436a25a5007b4f98262f8e8311e6acfb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a7d638c9a5bca41e7129446432e96cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-03-12更新
|
2253次组卷
|
8卷引用:山东省菏泽市2024届高三下学期一模考试数学试题
7 . 已知函数
,
,
.
(1)判断
是否对
恒成立,并给出理由;
(2)证明:
①当
时,
;
②当
,
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea987f231a61367682b6abb1d490860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c7743ab916fb33ca0d2fc597cfc672f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e653994b245fbdc2ac3458429c65e69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3add1679c27392a1a7f635723a4b36eb.png)
(2)证明:
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d005e2d92072f3ed9289c5bb80f55cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5494b7905201c6f627c12b85b8a369.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c8b04a43f618f95b4ad5474944a64c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd436cb785ccb4d29baa6bf70c10a09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6495c0fcf9672516f5cb8c5ef614df13.png)
您最近一年使用:0次
2024-03-12更新
|
1303次组卷
|
8卷引用:山东省菏泽市第一中学人民路校区2024届高三下学期2月月考数学试题
名校
8 . 已知函数
.
(1)若
,求证:
;
(2)讨论关于x的方程
在
上的根的情况.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43dea74af12e4b8564bf08c74f8a37c0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc895959e9bc92294dc9dd2263dbf0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
(2)讨论关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a910ceddf453ba57ee7fa09652f1ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cf818dd484cc4cebd40a5f28eb8e9f.png)
您最近一年使用:0次
2024-03-09更新
|
931次组卷
|
3卷引用:山东省菏泽市第一中学八一路校区2024届高三下学期2月月考数学试题
名校
9 . 已知函数
.
(1)当
时,求函数
在区间
上的最小值;
(2)讨论函数
的极值点个数;
(3)当函数
无极值点时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1ec5faecf8dcec50c879383ae93744.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f113f0953b99014fdf934fd88811cb.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e99c600ffe31feffbaea1e462d1528c3.png)
您最近一年使用:0次
2024-02-29更新
|
3629次组卷
|
5卷引用:山东省聊城市第一中学2023-2024学年高二下学期第一次阶段性检测数学试题
10 . 已知函数
.
(1)当
时,求
的单调区间;
(2)若函数
恰有两个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3d4e49babb9059d25e69fea2459f95.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be466586da8810ccfd811c59a747adb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedcf14b3a920c5bf766e7fddfb7d930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次