原式=lim(x->+∞)[x^n*e^(-ax)]
=lim(x->+∞)[x^n/e^(ax)]
=lim(x->+∞)[nx^(n-1)/(ae^(ax))](∞/∞型極限,應(yīng)用羅比達法則)
=lim(x->+∞)[n(n-1)x^(n-2)/(a²e^(ax))](∞/∞型極限,應(yīng)用羅比達法則)
.
=lim(x->+∞){n!/[(a^n)(e^(ax))]}(∞/∞型極限,應(yīng)用羅比達法則)
=n!/(a^n)*lim(x->+∞)[1/e^(ax)]
=n!/(a^n)*0(∵a>0)
=0