lim(x→∞)(1-2/x) (x+1)次方

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lim(x→∞)(1-2/x) (x+1)次方
lim(x→∞)(1-2/x) (x+1)次方

lim(x→∞)(1-2/x) (x+1)次方
lim(x→∞) (1 - 2/x)^(x + 1)
= lim(x→∞) [1 + (- 2/x)]^[(- x/2) · (- 2/x) · (x + 1)]
= {lim(x→∞) [1 + 1/(- x/2)]^(- x/2)}^[- 2(x + 1)/x],前面部分如同lim(x→∞) (1 + 1/x)^x = e
= e^lim(x→∞) [- 2(x + 1)/x]
= e^lim(x→∞) - 2 · (1 + 1/x)
= e^(- 2 · (1 + 0))
= e^(- 2)
= 1/e²

Lim [x^2/(x^2-1)]^x (x→∞) lim(1+x/x)2x (x→∞) lim(x)lim(x→∞) [(x-1)/(x+1)]^2x 为什么 lim(x->∞) {[(-2)/(x+1)]*2x} = -4 x/2-1lim(1-2/x)x→∞ lim(x→∞)(1-2/x) (x+1)次方 lim(x→∞)[1+(1/x)]^x/2 lim(x→∞)(1-2/x)^2x lim x→∞(2x+1)/(3x-4) lim x→∞ x-1/x^2 lim x→∞(1-2/x)^x= 求lim(√x^2+1)-x x→-∞ 求lim(x→0)x cos 1/x lim(x→∞)x^2/ (3x-1)的极限求极限lim x→∞ (x/(1+x))^x lim(x→+∞)(x+e^x)^(1/x) lim（ x→∞）（1+x / x)^3x lim x→1 x-1/x^2-x lim(x→0)e^x-x-1/x^2 lim(x→∞)[（x^3+x^2+x^1+1)^(1/3) - x] 的极限.