limx趋于0+,x^2[e^(1/x)]=

Question

limx趋于0+,x^2[e^(1/x)]=

Answer 1

lim(x→0+)x^2[e^(1/x)] (t=1/x)
=lim(t→∞)e^t/t^2 (∞/∞)
=lim(t→∞)e^t/(2t)
=0