推 yalin0413 :感謝R大如此詳細的解答~謝謝尼 02/27 17:26
※ 引述《yalin0413 (玲)》之銘言：
: lim (sinx)^x
: x→0+
: 這題用e去換之後~我怎麼算都怪怪的~~
: 拜託大家救救我!!!!
lim (sinx)^x = lim exp[xln(sinx)]
x→0+ x→0+
ln(sinx)
= lim exp[────]
x→0+ 1/x
ln(sinx)
= exp [lim ────]
x→0+ 1/x
cosx/sinx
= exp (lim ─────)
x→0+ -1/x^2
-x^2
= exp (lim ───)
x→0+ tanx
x
= exp [lim ─── lim (-x)]
x→0+ tanx x→0+
(綠色的地方是1)
= exp(0) = 1
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