名校
解题方法
1 . (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)
您最近一年使用:0次
名校
解题方法
2 . 若实数x﹑y、m
满足
,则称y比x接近m.
(1)若
比1接近0,求x的取值范围;
(2)对正实数a,b,如果
比
接近2,求证:当
时,
比
接近2;
(3)已知函数
等于
和
中接近0的那个值.写出函数
的解析式,并指出它的单调区间(结论不要求证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4a7dd81a499fbb8baf5a094c6c87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9965755486b6b0887a2fcd0dc16e702b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e1fbe0fb49725cf6d1e689ee8986d6.png)
(2)对正实数a,b,如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b52159c4f340e243c243988c9469106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd46e6f8f462d69e3b88c3245a7585d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d5750417af6a1d63b064c467414502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e778bb8ded9102f97acddffbc03130.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da4fcad0fbcfd1c4811d5f84a1727119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65d0fbf9e5420e150263e457676c80e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
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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)
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4 . 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.
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2010·广东·一模
名校
5 . 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
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1188次组卷
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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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