lim(x→∞)(x+2/x-2)^2x=?

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lim(x→∞)(x+2/x-2)^2x=?lim(x→∞)(x+2/x-2)^2x=?lim(x→∞)(x+2/x-2)^2x=?答:lim(x→∞)[(x+2)/(x-2)]^(2x)=lim(x

lim(x→∞)(x+2/x-2)^2x=?
lim(x→∞)(x+2/x-2)^2x=?

lim(x→∞)(x+2/x-2)^2x=?
答:
lim(x→∞) [(x+2)/(x-2)]^(2x)
=lim(x→∞) {[1+4/(x-2)]^[(x-2)/4+2/4] }^8
=lim(x→∞) {[1+4/(x-2)]^[(x-2)/4] }^8
=e^8