计算极限，最好用手写！谢谢

原式=lim(x->+∞) x^2*[(1+1/x)^x]*{[1+1/(x+1)]^(x+1)/[(1+1/x)^x]-1}
=lim(x->+∞) x^2*e*{e^ln{[1+1/(x+1)]^(x+1)/[(1+1/x)^x]}-1}
=e*lim(x->+∞) x^2*ln{[1+1/(x+1)]^(x+1)/[(1+1/x)^x]}
=e*lim(x->+∞) x^2*{(x+1)ln[1+1/(x+1)]-xln(1+1/x)}
令t=1/x
原式=e*lim(t->0+) (1/t^2)*{(1/t+1)ln[1+1/(1/t+1)]-(1/t)ln(1+t)}
=e*lim(t->0+) {(1+t)ln[(1+2t)/(1+t)]-ln(1+t)}/t^3
=e*lim(t->0+) [(1+t)ln(1+2t)-(2+t)ln(1+t)]/t^3
=e*lim(t->0+) [ln(1+2t)+(2+2t)/(1+2t)-ln(1+t)-(2+t)/(1+t)]/3t^2
=e*lim(t->0+) [ln(1+2t)-ln(1+t)+1/(1+2t)-1/(1+t)]/3t^2
=e*lim(t->0+) [2/(1+2t)-1/(1+t)-2/(1+2t)^2+1/(1+t)^2]/6t
=e*lim(t->0+) [4/(1+2t)^2-1/(1+t)^2]/6
=e/2