lim (1+2/x)^2 x→无穷大

问题描述:

lim (1+2/x)^2 x→无穷大

lim(x→∞) (1+2/x)^(x+2)
=lim(x→∞) (1+2/x)^[(x/2)*2+2)]
=lim(x→∞) [(1+2/x)^(x/2)]^2*lim(x→∞) (1+2/x)^2
=e^2