Re: [微積] 拜託能不能給我點提示

[Eliphalet (蘇格蘭狗餅)]

※ 引述《x0940640406 (smile)》之銘言：
: http://i.imgur.com/H2Wf9gN.jpg
: 4.10.13
: 求提示啊～～～ 完全摸不著頭緒



  4.  對 x > 0 ， x/sqrt(1-cos(x)) = 1/sqrt( (1-cos(x))/x^2 )

                                   -> 1/sqrt(1/2) = sqrt(2) as x->0+



 10.  x^2/sin^2(x/3) = 9 * (x/3)^2 / sin^2(x/3) -> 9 as x->0



 13.  (1-x^2)/sin(pi*x) =  (1-x^2)/(x-1) * (x-1)/(sin(pi*x) - sin(pi))

                        -> -2 * ( pi * cos(pi) )^(-1)

                        = 2/pi as x->1

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推 apologize   : 第4題是0吧
   你確定是 0 嗎？

   x = 10^(-1) ,  x/sqrt(1-cos(x)) ≒ 1.414803

   x = 10^(-2) ,  x/sqrt(1-cos(x)) ≒ 1.414219

   x = 10^(-3) ,  x/sqrt(1-cos(x)) ≒ 1.414214

   ...
※ 編輯: Eliphalet (114.46.212.176), 09/22/2015 16:22:55