i.e. limit for the numerator is x→∞limx=∞ and limit for the denominator is x→∞limex=∞ Let's take derivatives of the numerator and denominator until we eliminate indeterninateness. x→∞lim(xe−x) = x→∞lim(dxdexdxdx) = x→∞lim(2xe−x) = x→∞lim(2xe−x) = 0 It can be seen that we have applied Lopital's rule (we have taken derivatives with respect to the numerator and denominator) 1 time(s)