作者nomorethings (花哈哈哈)
看板NTUMath91
標題Re: [請益] 想請問一題極限
時間Tue Mar 15 23:04:47 2005
sin x 1/x^2
lim ( ─── )
x-> 0 x
ln(sin(x)/x)
=exp ( lim ------------ )
x^2
X X*cosX-sinX
----*-----------
sinX X^2
=exp ( lim --------------------)
2X
X*cosX-sinX
-----------
X*sinX
=exp ( lim -------------------- )
2X
X*cosX-sinX
=exp ( lim -------------------- )
2*sinX*X^2
cosX-X*sinX-cosX
=exp ( lim -------------------- )
2*cosX*X^2+4*X*sinX
-sinX-X*cosX
=exp ( lim ----------------------------------- )
4*X*cosX-2*sinX*X^2+4*sinX+4*X*cosX
-sinX-X*cosX
=exp ( lim -------------------------- )
8*X*cosX-2*sinX*X^2+4*sinX
-cosX-cosX+X*sinX
=exp ( lim ------------------------------------------ )
8*cosX-8*X*sinX-4*X*sinX-2*cosX*X^2+4*cosX
- 1 - 1 + 0
=exp ( ------------------------------------------ )
8*1 - 0 - 0 - 0 + 4
-2 -1/6
=exp ( ----- ) = e
12
唔...
希望沒有錯誤拉ＸＤＤ
有錯的話還望大家指教 ｍ（＿＿）ｍ
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