题目内容
已知函数f(x)=A
(A>0,
>0,0<
<
,且y=f(x)的最大值为2,其
图象相邻两对称轴间的距离为2,并过点(1,2).
(1)求
;
(2)计算f (1) + f (2) +… + f ( 2 008 ).
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135672532.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135703201.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135718209.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135734218.gif)
图象相邻两对称轴间的距离为2,并过点(1,2).
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135718209.gif)
(2)计算f (1) + f (2) +… + f ( 2 008 ).
解:(1)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135765871.gif)
的最大值为2,
.![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135874408.gif)
又
其图象相邻两对称轴间的距离为2,
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136015572.gif)
.
过
点,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136280534.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136311586.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136327591.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136358516.gif)
又![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135890183.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136405433.gif)
.…………………………………6分
(
2)
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136467775.gif)
.
又
的周期为4,
,
…………………
……………12分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135765871.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135781417.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135796250.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135874408.gif)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135890183.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135999257.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136015572.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136030953.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136062410.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136264265.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136280534.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136311586.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136327591.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136358516.gif)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190135890183.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136405433.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136420398.gif)
(
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/2014082319013643672.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136452402.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136467775.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136639791.gif)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136654447.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136670479.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190136686800.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/2014082319013670165.gif)
略
![](http://thumb.zyjl.cn/images/loading.gif)
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