1 . 设
、
、
是方程
的三个根,
且
.
⑴求
的整数部分;
⑵求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21db4e349477acece26642653c1876a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f5ae6592d62f1efb53e37647407722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c799b0a577c0c25274bc0554ea2753ea.png)
⑴求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
⑵求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe9c48c9f8e12cfb0ac44e7f4e919e1.png)
您最近一年使用:0次
2014高三·天津·竞赛
2 . 设函数
,证明:
(1)当
时,
;
(2)若数列
满足
,则数列
递减,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887878406cf6cb0389ff7d45129f5918.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9d189d2ade2eb7ea55b8ebfa51c56d.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36270e0f17e1f9128b670491a04c7d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2beb081ae289ae8d192f39312a3437ef.png)
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2011高三·天津·竞赛
3 . 设
、
、
、
、
、
为实数,且
对任意的实数
成立.证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dcc8b824bf93f5981bfd1fd3d1a71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9723d411b2a0409c768eb8bbbe2f0bc0.png)
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4 . 已知函数
.
(1)是否存在实数
、
,使得函数
的定义域和值域都是
?若存在,请求出
,
的值;若不存在,请说明理由.
(2)若存在实数
,
,使得函数
的定义域是
,值域是
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9780822e89d640bff65253bf5009052d.png)
(1)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f9fcab2886322d40bb5b52d997984fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f9fcab2886322d40bb5b52d997984fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030052a6936e5136de625c65eea375af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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5 . 已知函数
.
(1)试求函数
的解析式;
(2)若
时,直线
与曲线
交于三个不同的点,试确定
与
的关系式,并画图表示以
、
为坐标的点
所在的区域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d62a8d50030d57b21f524b80ea0c2d7.png)
(1)试求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0ebfd385ccb5413269d581278925fd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed2f5e11cef1a7062aac81b72d70b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e136e7637543c8ae92c8dcd55b31924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
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