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Re:谁能告诉我你们怎么证明R*sin(L'/2R)在(L/2,inf)区间内是关于R的单调函数的？学的知识都还给老师了。。。

Posted by forif at 2014-03-04 13:38:21 on Problem 1905
In Reply To:谁能告诉我你们怎么证明R*sin(L'/2R)在(L/2,inf)区间内是关于R的单调函数的？学的知识都还给老师了。。。 Posted by:forif at 2014-03-04 12:17:01 
晕
求导之后是f'=sin(L'/2x)-(L'/2x)cos(L'/2x),让f'=0得
tan(L'/2x)=(L'/2x)
因为0<L'/2x<1,tan(x)在（0，1）上恒小于x，所以导函数大于0，单调。。。
中间细节好像有点糙。。。
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