What is $\displaystyle\lim_{x\to\infty}\dfrac{x^3}{e^x}$?

Core Concept

The form is $\dfrac{\infty}{\infty}$. Repeated L'Hôpital's rule gives $\dfrac{3x^2}{e^x}\to\dfrac{6x}{e^x}\to\dfrac{6}{e^x}\to 0$, because the exponential outgrows the power.