这式为什么能用洛必达,∞/1 型

limx→0 (1+x)^(1/x^3),
=limx→0 [(1+x)^(1/x)]^(1/x^2),
=limx→0 e^(1/x^2),
——》原式=limx→0 (1/x)/[e^(1/x^2)],(∞/∞型,洛必达法则求导)
=limx→0 (-1/x^2)/[e^(1/x^2)*(-2/x^3)]
=limx→0 x/[2*e^(1/x^2)]
=0/∞
=0.