【题文】已知函数(),数列满足,,.则与中,较大的是 ;,,的大小关系是
题型:难度:来源:
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021341-70636.png)
(
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021341-75817.png)
),数列
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021341-22796.png)
满足
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021342-91979.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021342-37342.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021342-45406.png)
.则
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021343-20047.png)
与
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021343-44441.png)
中,较大的是
;
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021343-32267.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021344-29430.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021344-57604.png)
的大小关系是
.
答案
【答案】
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021343-20047.png)
;
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021344-61593.png)
解析
【解析】
试题分析:函数
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021345-49853.png)
是单调递减的,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021346-74416.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021346-96460.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021347-21227.png)
,因为
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021347-49723.png)
,
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021347-76349.png)
,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021348-25501.png)
那么有
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021348-55948.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021348-68482.png)
,所以则
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021343-20047.png)
与
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021343-44441.png)
中,较大的是
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021349-45452.png)
.同理可得
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021349-78152.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021350-58847.png)
,所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021350-61208.png)
从第一项开始,函数值先增大后减小再增大
再减小,最后趋于平稳值,奇数项的值慢慢变大趋于平稳值,偶数项慢慢变小趋于平稳值,所以偶数项的
值总是大于奇数项的值,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021343-32267.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021344-29430.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021344-57604.png)
的大小关系是
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021344-61593.png)
.
考点:1.数列的递推公式;2.数列的函数特性;3.指数函数的单调性
举一反三
【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021321-15295.png)
是
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021322-43340.png)
上的偶函数,且在
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021322-85129.png)
上为减函数,若
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021323-31267.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021323-27288.png)
,则( )
【题文】在
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021253-43063.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021253-60716.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021253-17872.png)
这三个函数中,当
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021254-62436.png)
时,使
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021254-27183.png)
恒成立的函数个数是:( )
A. 0 | B.1 | C.2 | D.3 |
【题文】设定义域为R的函数
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021242-22419.png)
满足下列条件:对任意
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021242-82068.png)
,且对任意
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021242-32113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021243-23730.png)
,当
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021243-85954.png)
时,有
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021243-99842.png)
.给出下列四个结论:
①
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021244-22506.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021244-86662.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021244-97495.png)
④
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326021245-19609.png)
其中所有的正确结论的序号是____________.
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