lim(x->0){[1/(1+2x)]^(1/x)}=lim(x->0){[1+(-2x)/(1+2x)]^[((1+2x)/(-2x))*((-2)/(1+2x))]}=e^{lim(x->0)[(-2)/(1+2x)]} (应用重要极限lim(z->0)[(1+z)^(1/z)]=e)=e^(-2)=1/e².