limx->无限 [x^2/(x^2+1)]^x=?
问题描述：
limx->无限 [x^2/(x^2+1)]^x=?
答
答：
lim [x^2/(x^2+1)]^x
=lim [1-1/(x^2+1)]^x
=lim (1-1/x^2)^x
=lim {[(1-1/x)^(-x)*(-1)]*(1+1/x)^x} x→∞
=(1/e)*e
=1答案是e^-1/2!答：lim [x^2/(x^2+1)]^x=lim [1-1/(x^2+1)]^x=lim (1-1/x^2)^x令t=x^2>0，x=√t=lim (1-1/t)^(√t)=lim [(1+1/(-t))^(-t)]^(-1/2)=e^-(1/2)我怀疑这个解答，因为x趋于无穷有正无穷和负无穷....