1 . 已知,
.
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78fb5c966bea9ff5e7579181a20617ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03bbcfce2a8c6901741b3644c4c493c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e477c321cb0620f5c20e37763775221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032b1b7450d05f5d5ff2e9df74e3792e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06aaadbbbd40e7259ee76cbfeaebc25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176c580ac372c687eea2f4dc1eeb1f20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb342c191aa0c8a897926a001497397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77c0049a833006a7a252dbdfed053cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4474e5ea33b1bd22bfb0abb9e76a3046.png)
您最近一年使用:0次
名校
2 . 已知函数
,取点
,过其作曲线
切线交
轴于点
,取点
,过其作曲线
作切线交
轴于
,若
,则停止操作,以此类推,得到数列
.
(1)若正整数
,证明 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456ed50e1ec3e101f32e930614eebcf9.png)
(2)若正整数
,试比较
与
大小;
(3)若正整数
,是否存在k使得
依次成等差数列? 若存在,求出k的所有取值,若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590eeefa9b43063edc41ac94f5e02956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b707db9c9766efcc91c87824399b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590eeefa9b43063edc41ac94f5e02956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0b0c4e9dcbfc7a5d04f62fc547ec09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5465bc85798c3bfc7905e58578d251c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590eeefa9b43063edc41ac94f5e02956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b0a15fde3d36d7530e70cc4a5730ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a1aca2793cb07162e29c75a388fe70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456ed50e1ec3e101f32e930614eebcf9.png)
(2)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf1e4c54010243a8f6c9a1c8482143.png)
(3)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835c74bbb8c61dd2d2f008664a8c8810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41dd42e4f493477fb0f36137893d4d06.png)
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3 . 定义:设
和
均为定义在
上的函数,它们的导函数分别为
和
,若不等式
对任意实数
恒成立,则称
和
为“相伴函数”.
(1)给出两组函数,①
和
②
和
,分别判断这两组函数是否为“相伴函数”(只需直接给出结论,不需论证);
(2)若
是定义在
上的可导函数,
是偶函数,
是奇函数,
,证明:
和
为“相伴函数”;
(3)
,写出“
和
为相伴函数”的充要条件,证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c325e7c3a16e7e6fe3835e24d093b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(1)给出两组函数,①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeea68b05083aaf5bc84b63ddea32fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61c6ee8a90940db217d0ed2202cfa3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3d9ab1739e4f997071a7d558bb6afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4985909410ebcf6be0cf45b2057c7eaf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3970e1ef97656c4db82edf2b75b000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2e5e73fcd10764ccd2a44bae179986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56877b5653c96790a2ae9482f4e55e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
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名校
4 . 已知
,
.
(1)求函数
的单调区间;
(2)①容易证明
对任意的
都成立,若点
的坐标为
,
、
为函数
图像上横坐标均大于1的不同两点,试证明:
;
②数列
满足
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8b8645a4cd5e41664b349bc1d2c4ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a20457d180264f78d611dc7893d735.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)①容易证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832f2474efe89961ef41e884da7660c.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/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f662ae83689b19b2a4a9b37a3a9b70.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4b74ed1cf474f645df5ef7100c0d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfb19f0c37a72b33083ae9319f11a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3360833401d932ae800aefe4ae8f24.png)
您最近一年使用:0次
2023-08-03更新
|
563次组卷
|
4卷引用:上海市南洋模范中学2024届高三上学期10月月考数学试题
5 . 已知数列
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008348710d58f60262da3759afd4e606.png)
A.当![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-06-19更新
|
10963次组卷
|
23卷引用:上海市育才中学2024届高三上学期10月调研数学试题
上海市育才中学2024届高三上学期10月调研数学试题上海市南洋模范中学2024届高三上学期10月月考数学试题山西省晋城市第一中学校2024届高三上学期8月月考数学试题上海市普陀区晋元高级中学2024届高三上学期秋考模拟数学试题2023年北京高考数学真题专题05数列(成品)(已下线)2023年北京高考数学真题变式题6-10(已下线)北京十年真题专题06数列北京十年真题专题06数列(已下线)模块四 第五讲:利用导数证明不等式【练】(已下线)第1讲:数列的函数性质应用【练】(已下线)数列的综合应用(已下线)第3讲:数列中的不等问题【练】(已下线)第4讲:数列中的最值问题【练】(已下线)第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)专题05 数列 第三讲 数列与不等关系(分层练)(已下线)重难点10 数列的通项、求和及综合应用【九大题型】(已下线)专题28 数列的概念与简单表示(已下线)专题06 数列小题(理科)-2(已下线)专题05 数列小题(7类题型,文科)河南省信阳高级中学2024届高三5月测试(一)二模数学试题北京市东直门中学2023-2024学年高一上学期期中考试数学试题(已下线)专题06 数列在高考中的考法(难点,十一大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)
名校
解题方法
6 . 设函数
,
.
(1)记
,
,
,
.证明:数列
为等差数列;
(2)设
.若对任意
均有
成立,求m的最大值;
(3)是否存在正整数
使得对任意
,
,都有
成立?若存在,求
的最小可能值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d40624fc4d5a669a76185052ee6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0ec3c50f8ff3bbb30ba0a0962073f2.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6922d957239774592783e33853982fe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c0a98e6d574ec3702340e64bba6c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3100ae0145d424c88cf5cf7c0e394241.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a1f8ed373823d79f44edbef03e1984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2314d72ec216ff0e787741483524efaf.png)
(3)是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0166ef16246534081188fce28684b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a5b858803482915e35ad5a57dcddb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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名校
解题方法
7 . 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
|
725次组卷
|
4卷引用:上海市七宝中学2023届高三下学期4月月考数学试题
名校
解题方法
8 . 已知实数
,
,
.
(1)求
;
(2)若
对一切
成立,求
的最小值;
(3)证明:当正整数
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9e5b7f6208a13f357be15e7d710ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f146c48c81d7148fa0acbb24e9716e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aecd30fc6668e650986e1c33b0e4732.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3ec7ada52f4850719a970aeb59ca16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1415277a2abd787827778054bd134d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2d628fffa16f2afab468d95f5c652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)证明:当正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36358fa9a7718a7337f35e90592fc16d.png)
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2023-05-10更新
|
666次组卷
|
3卷引用:上海市徐汇中学2023-2024学年高三下学期3月月考数学试题
22-23高三下·上海浦东新·阶段练习
名校
解题方法
9 . 若定义域为D的函数
使得
是定义域为D的严格增函数,则称
是一个“T函数”.
(1)分别判断
,
是否为T函数,并说明理由;
(2)已知常数
,若定义在
上的函数
是T函数,证明:
;
(3)已知T函数
的定义域为
,不等式
的解集为
.证明:
在
上严格增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)分别判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7145da612cce6f52bd346949d2c79618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/842f20228995cb020d8963f332d12189.png)
(2)已知常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdbe529a618d8ecd69c147adb5c4fd9.png)
(3)已知T函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02a5802f50d0bac17f22f9a18f3d5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
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名校
10 . 已知函数
.
(1)求函数
在点
处的切线方程;
(2)已知
对于
恒成立,证明:当
时,
;
(3)当
时,不等式
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ab70ac1f081eead97f4cb82842e024.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1c98c9dcab33fe2908ebff7bbec97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9322dd8f56b5f8d2c667fdf0d4a9f9aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22165fb1166b885fec563eb95b778882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22165fb1166b885fec563eb95b778882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446353068f50cd5bc63a01a914cf288d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-03-11更新
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553次组卷
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2卷引用:上海市建平中学2023届高三下学期3月月考数学试题