真题
解题方法
1 . A是由定义在
上且满足如下条件的函数
组成的集合:①对任意的
,都有
;②存在常数
,使得对任意的
,都有
.
(1)设
,证明:
;
(2)设
,如果存在
,使得
,那么这样的
是唯一的;
(3)设
,任取
,令
,证明:给定正整数k,对任意的正整数p,不等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de71d25c72850e383a4c841eed0db99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2775ffdf695af2d263f0ea93ac5904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4031c9cbbcbbecfc0a8ca5490647e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5d880d349c00a3f81f830bb35e1d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d03b29af4e3206af656a142d17657f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799650ddf5fb8e7c91cf59163aa1b7a4.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1dbdb8423d86a92629b081ae2b2154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0324fecb070287715e3e8f2322056922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a5528f643fe7e0449e48c8f81b16b01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cb6b97b664d70c3c3b9e2b88c80b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e599070e5874ed4a9478f5260b98e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0d7024ce3371628f09963f9a976ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dcca902b1982e13aeea5d094bb6016.png)
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