2010·广东·一模
名校
1 . 对于定义在区间D上的函数
,若存在闭区间
和常数
,使得对任意
,都有
,且对任意
∈D,当
时,
恒成立,则称函数
为区间D上的“平底型”函数.
(Ⅰ)判断函数
和
是否为R上的“平底型”函数? 并说明理由;
(Ⅱ)设
是(Ⅰ)中的“平底型”函数,k为非零常数,若不等式
对一切
R恒成立,求实数
的取值范围;
(Ⅲ)若函数
是区间
上的“平底型”函数,求
和
的值.
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2a2d903ba240a8b9a5ffc89d253c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8fcc03f1fbc04e581c54d481543a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82639cc42b3278ddb550fcd40550cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9287c65e8e6c68fd2a43cd68a4ed308e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e65ce6beb859d217affa006e8bd355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅰ)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e64da1f043ad0c3fd44f6c24eaa6459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca2d1b039514228cb725445f3d6f8df.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d9d2218ca8690645409c8c93f8d7659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb1d808cf4ff5ea1a3399c2d25656a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(Ⅲ)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46bf94f9a3b0a0cc75158b6073ffc9eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a7ab1aba1cdf4453848ccece383b12e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
.
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2016-11-30更新
|
1188次组卷
|
5卷引用:2010年普通高等学校招生全国统一考试预测卷(广东卷)理科试题
(已下线)2010年普通高等学校招生全国统一考试预测卷(广东卷)理科试题(已下线)广东省珠海一中09-10学年高二下学期期末考试理科数学试题(已下线)2011届河北省唐山一中高三第二次调研考试数学理卷上海市向明中学2015-2016学年高一上学期期中数学试题江苏省盐城市建湖县上冈高级中学2018-2019学年高一上学期期中数学试题
20-21高二上·全国·单元测试
解题方法
2 . 设集合W由满足下列两个条件的数列{an}构成:①
;②存在实数M,使an≤M(n为正整数)
(1)在只有5项的有限数列{an}、{bn}中,其中a1=1,a2=2,a3=3,a4=4,a5=5,b1=1,b2=4,b3=5,b4=4,b5=1,试判断数列{an}、{bn}是否为集合W中的元素;
(2)设{cn}是等差数列,sn是其前n项和,c3=4,s3=18,证明数列{sn}∈W,并写出M的取值范围;
(3)设数列{dn}∈W,对于满足条件的M的最小值M0,都有dn≠M0(n∈N*)求证:数列{dn}单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc75a9da38151496ca2adce84a977b96.png)
(1)在只有5项的有限数列{an}、{bn}中,其中a1=1,a2=2,a3=3,a4=4,a5=5,b1=1,b2=4,b3=5,b4=4,b5=1,试判断数列{an}、{bn}是否为集合W中的元素;
(2)设{cn}是等差数列,sn是其前n项和,c3=4,s3=18,证明数列{sn}∈W,并写出M的取值范围;
(3)设数列{dn}∈W,对于满足条件的M的最小值M0,都有dn≠M0(n∈N*)求证:数列{dn}单调递增.
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解题方法
3 . 定义:记
为
这
个实数中的最小值,记
为
这
个实数中的最大值,例如:
.
(1)求证:
;
(2)已知
,求
的最小值;
(3)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e824d15bf3a32ceafbf100e4bf3b6a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bee78f4561539faf2b6f382ce5f94f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75c8ecbf2c10fd090d119238cbfbb1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bee78f4561539faf2b6f382ce5f94f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883d52e4bbbec68682117456d078a2ca.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/543743dde06d90ad5da3632ef0792f59.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aede98f52c2cd9911b09d7faf08a0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd44b30ab4f8d40eb4eb30e8f9f807fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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4 . 设
为下述正整数
的个数:
的各位数字之和为
,且每位数字只能取
,
或![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(1)求
,
,
,
的值;
(2)对
,试探究
与
的大小关系,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(2)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac657ea5bbf4b237a30e4074c76cc81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd12570de0a4883407dc50eea28e011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3ada10cd62cec32c5ffc7bd17d3599.png)
您最近一年使用:0次
名校
解题方法
5 . (1)若
,
,求证:
;
(2)设
,求函数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829c3146484a77b8597a60f806ce8ee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2aa5e48ef4cc10678706d9883e7a0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031ede0c2bfeb8bfb8b347a2e7cd3bbc.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fecaefda8567646f10d76668293d845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7de8538ee943759e297736b8ac2845.png)
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6 . 已知
,
(其中
是自然对数的底数),求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18478e45096362e297359fe9345b073a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fd5a05aae4f1a7d8a8e32e80ca7263.png)
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解题方法
7 . 已知关于x的不等式
的解集为A.
(1)若
,求A;
(2)若
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0cdf35fd256033009811b269682893.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843c3f388a75bf981c11ca947a86e5fa.png)
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解题方法
8 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d85ab9b6287f810bfb1443ba4a98065.png)
(1)解不等式
;
(2)
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d85ab9b6287f810bfb1443ba4a98065.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fbc901cbdb68130ddac3174583dd93c.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5931095eb29d9d6b55ed9fa32a4ef1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-03-02更新
|
149次组卷
|
2卷引用:广西南宁市第二中学2019-2020学年高一上学期期中数学试题
13-14高一下·广东揭阳·期中
名校
9 . 已知定义域为
的函数
同时满足以下三个条件:
(1) 对任意的
,总有
;(2)
;(3) 若
,
,且
,则有
成立,则称
为“友谊函数”,请解答下列各题:
(1)若已知
为“友谊函数”,求
的值;
(2)函数
在区间
上是否为“友谊函数”?并给出理由.
(3)已知
为“友谊函数”,假定存在
,使得
且
, 求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1) 对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376168658dbe7f5b7f4d75fb1db545a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12aae852c3129efc16934aefc54201f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cd2fe62ffe3caa1c6f7976851c9dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2f51cd760aeff9365b51e9a85b41e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27928aa83370ffb7e137019ff03c3e58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)若已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54b6a060d6c51a328341df76013bd89.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078d5da73e5aa679bc163820b7b73f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc0414f6c290d1dc3678ba41b4620f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c22b0b866e6181ac3c39c9c1db91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4415137475716480dfb80957285379f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73bc955d158efde0bdd62d14a60a65e3.png)
您最近一年使用:0次
2016-12-03更新
|
1861次组卷
|
3卷引用:2013-2014学年广东省揭阳一中高一下学期期中学业水平测试数学试卷
(已下线)2013-2014学年广东省揭阳一中高一下学期期中学业水平测试数学试卷湖南师范大学附属中学2017-2018学年高一上学期第一次阶段性检测数学试题湖北省武汉为明学校2019-2020学年高一上学期第一次阶段考试数学试题
名校
10 . 定义:若函数
对任意的
,都有
成立,则称
为
上的“淡泊”函数.
(1)判断
是否为
上的“淡泊”函数,说明理由;
(2)是否存在实数
,使
为
上的“淡泊”函数,若存在,求出
的取值范围;不存在,说明理由;
(3)设
是
上的“淡泊”函数(其中
不是常值函数),且
,若对任意的
,都有
成立,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bac2cb668c70578fc0169549e1625f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b59c27d3269eb73d26c435228cd841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18bdb082158616960251df52ae79f863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9653a7d78d57ffcab20bb38f5bc818b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75c3204dcb6b697db534514558111f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d0c9d13770863f59ea9fa45488de63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb29bb7ac50f37b9a0f40b35c8081c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e092b576de88477bd378f644b0f082a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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