作者iamhido (.....................)
看板trans_math
标题Re: 一题极限问题?
时间Tue Apr 19 11:09:17 2005
※ 引述《anson0810 (奇  )》之铭言：
: lim
: x->pi/4 (x-pi/4)tan2x
: 请问一下这一题的答案是0吗?
令y=x-pi/4
lim
则原式= y->0 y*tan(2y+pi/2)
lim
= y->0 y*{-cot(2y)}
lim
= y->0 -cot(2y)/(1/y)
lim
= y->0 2(csc2y)^2/(-1/y^2)
lim
= y->0 (-2)*{y^2/(six2y)^2}
lim
= y->0 (-2)*(1/4)(2y/six2y)^2
= (-1/2)(1)^2=-1/2
#
参考看看罗~~
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1F：推 Elfiend:原式改写成(x-π/4)/cot2x再罗必达的算式很简短220.139.177.197 04/21