limx趋于0+,x^2[e^(1/x)]=

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

limx趋于0+,x^2[e^(1/x)]=
limx趋于0+,x^2[e^(1/x)]=

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