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

来源：学生作业帮助网编辑：作业帮时间：2024/04/30 21:11:03

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

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

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

求极限lim x→∞ (x/(1+x))^x lim(x→+∞)(x+e^x)^(1/x) lim(1+x/x)2x (x→∞) Lim [x^2/(x^2-1)]^x (x→∞) lim（ x→∞）（1+x / x)^3x 求极限lim(x→0)sinxsin(1/x);lim(x→∞)(arctanx/x) lim(x-cosx)/x x→-∞ lim(x→∞)(cos1/x)^x lim(0-∞)/(x+1) lim(x)lim(x→∞) [(x-1)/(x+1)]^2x 为什么 lim(x->∞) {[(-2)/(x+1)]*2x} = -4 lim x→ lim(x-1)[e^(1/x)-1],x→+∞ x/2-1lim(1-2/x)x→∞ lim(x→∞)(1-2/x) (x+1)次方 lim(x→∞) (xsin(1/x)+1/x(sinx)) lim(x→∞)[1+(1/x)]^x/2 x→+∞,lim（1+a/x)^x=? lim(x→∞)x[ln(x-1)-lnx]