limx->无限 [x^2/(x^2+1)]^x=?

limx->无限 [x^2/(x^2+1)]^x=?
limx->无限 [x^2/(x^2+1)]^x=?

limx->无限 [x^2/(x^2+1)]^x=?
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

取指数 上下进行