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lim(x)lim(x→∞)[(x-1)/(x+1)]^2x为什么lim(x->∞){[(-2)/(x+1)]*2x}=-4
题目详情
lim(x)lim(x→∞) [(x-1)/(x+1)]^2x
为什么 lim(x->∞) {[(-2)/(x+1)]*2x} = -4
为什么 lim(x->∞) {[(-2)/(x+1)]*2x} = -4
▼优质解答
答案和解析
lim(x->∞) [(x-1)/(x+1)]^2x
=lim(x->∞) [ 1 + (-2)/(x+1)]^[(x+1)/(-2)]*{[(-2)/(x+1)]*2x}
=lim(x->∞) {[ 1 + (-2)/(x+1)]^[(x+1)/(-2)]}^{[(-2)/(x+1)]*2x}
∵ lim(x->∞) {[ 1 + (-2)/(x+1)]^[(x+1)/(-2)]} = e
lim(x->∞) {[(-2)/(x+1)]*2x} = -4
= e^(-4)
=lim(x->∞) [ 1 + (-2)/(x+1)]^[(x+1)/(-2)]*{[(-2)/(x+1)]*2x}
=lim(x->∞) {[ 1 + (-2)/(x+1)]^[(x+1)/(-2)]}^{[(-2)/(x+1)]*2x}
∵ lim(x->∞) {[ 1 + (-2)/(x+1)]^[(x+1)/(-2)]} = e
lim(x->∞) {[(-2)/(x+1)]*2x} = -4
= e^(-4)
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