令y=(x+1/x-1)^x lny=x[ln(x+1)-ln(x-1)] ,
limlny= limx[ln(x+1)-ln(x-1)]=lim[ln(x+1)-ln(x-1)]/(1/x)=lim[1/(x+1)-1/(x-1)]/(-1/x^2)
=lim{2x^2/(x^2-1)=lim2/(1-1/x^2)=2,所以 limlny=2=lnlimy
limy=e^2明白了！