名校
1 . 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)
您最近一年使用:0次
2 . 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
3 . 已知函数
,
.
Ⅰ
记
在
上的最大值为M,最小值为m.
若
,求a的取值范围;
证明:
;
Ⅱ
若
在
上恒成立,求a的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e75613d81de6fe1309da3f046f8a366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980a8c4eb822aeb591ceacfe8a7aaa11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a29726cb09e82862db881a3258c34b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/372470aee75717ec33c53c3434eb126d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ea4f4e439a11a84a4445b4c8c0c96f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18eca8193d91e13a240dec14be339cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b8845bd03ac01a26ef57851a8764cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c1472bd3540ad41abb5b0d8c4d8a66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35246b1f7e094e6e7ea093f2f53a1a3f.png)
您最近一年使用:0次
4 . 已知函数
,不等式
的解集为
.
(1)求
的值;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2caaa9f5fda86a33f067300545196d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aac626c05da00b3d40cf260cb95f4a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad4099ebc64187f7de0c49e84d6185b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7daa23c80e645fa52021bf6b2c6bf642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
5 . 在直角坐标系中,定义
之间的“直角距离”:
.若点
,
为直线
上的动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afcf3f2dd70267daf292fd7affbe3cf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b175cbe0bf64d7852e3270158d29bad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85dd382fa447b567a9de87cac1990d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ff7e0ef1f622120cc1b18e9d3e80ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abd1ceef6e219ee7dfa3f72f3014e92.png)
(Ⅰ)解关于的不等式
;
(Ⅱ)求的最小值.
您最近一年使用:0次
6 . 选修4-5:不等式选讲
在平面直角坐标系中,定义点
、
之间的直角距离为
,点
.
(1)若
,求
的取值范围;
(2)当
时,不等式
恒成立,求
的最小值.
在平面直角坐标系中,定义点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2009bbb16442829022f71f67954f6706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e5706dc8e7751b5a8163359a648f14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7a19707421ee0a0db45f5b89695b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb15fec0f2b74cc3e94e5305eaff0b0a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf1e7659c52892524c77881ca85ccc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9985ad1358d0fddcb8bfc99deb95bf1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091c82cf9c6f1a6037aededab53f087d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2010·广东·一模
名校
7 . 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)
.
您最近一年使用:0次
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
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