Re: [極限] 求極限是否存在

作者: a016258 (憨)   2013-10-29 14:28:39
※ 引述《kylestyle (最近有點煩)》之銘言:
: lim. (csc x)^(sinx)^2
: x→0
: 求板上大大解答 感謝
(省略 x->0)
= lim exp ( -(sinx)^2 * ln(sinx) )
=> lim ( -ln(sinx) / (cscx)^2 )
= lim ( -(cosx/sinx) / -2cscx^2 * cotx )
= lim ( (1/2) ( cosx / sinx ) * [(sinx)^3 / cosx]
= lim ( (1/2) * (sinx)^2 ) = 0
=> exp(0) = 1
有錯還請不吝指正...XD
作者: BaBi (迅雷不及掩耳盜鈴)   0000-00-00 00:00:00
第四行那邊怪怪的, 最後應該是(sin)^2/2~

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