令1/a=-2/xx=-2a所以原式=lim(a→∞)(1+1/a)^(-2a-2)=lim(a→∞)1/(1+1/a)^(2a+2)=lim(a→∞)1/[(1+1/a)^a]^2*(1+1/a)^2=1/e^2
lim(x→∞)(1-2/x)^(x-2)=lim(x→∞)(1-2/x)^x/lim(x→∞)(1-2/x)^(-2)=lim(x→∞)[(1-2/x)^(-x/2)]^(-2)=1/e^2
