Re: 極限問題？
※ 引述《acgrun (acgrun)》之銘言：
: X^2 - 81
: 1.lim __________ = 108
: X->9 √x – 3
: X
: 2.lim _________________ = -3
: X->0 1 - 立方根(x+1)
1 - (x+1)
= (1^(1/3))^3 - ((x+1)^(1/3))^3
= (1^(1/3) - (x+1)^(1/3))(1^(2/3) + (1^(1/3))((x+1)^(1/3)) + (x+1)^(2/3))
= (1 - (x+1)^(1/3))(1 + (x+1)^(1/3) + (x+1)^(2/3))
x
lim -----------------
x→0 1 - (x+1)^(1/3)
(x)(1 + (x+1)^(1/3) + (x+1)^(2/3))
= lim --------------------------------------------------
x→0 (1 - (x+1)^(1/3))(1 + (x+1)^(1/3) + (x+1)^(2/3))
(x)(1 + (x+1)^(1/3) + (x+1)^(2/3))
= lim ------------------------------------
x→0 1 - (x+1)
(x)(1 + (x+1)^(1/3) + (x+1)^(2/3))
= lim ------------------------------------
x→0 -x
= lim (-1)(1 + (x+1)^(1/3) + (x+1)^(2/3))
x→0
= (-1)*(1 + 1 + 1) = (-1)*(3) = 3
: 答案有了，可是不知道是如何來的，
: 可用立方差公式，但是不知道如何解？
: 可列出詳細過程嗎？謝謝
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