lim(x)lim(x→∞) [(x-1)/(x+1)]^2x 为什么 lim(x->∞) {[(-2)/(x+1)]*2x} =_数学解答

lim(x)lim(x→∞) [(x-1)/(x+1)]^2x
为什么 lim(x->∞) {[(-2)/(x+1)]*2x} = -4

人气：243 ℃　时间：2020-10-02 05:37:42

解答

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...