Question

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→[infinity] x4e−x3

Answer 1

Here the l'Hospital's Rule is appropriate, as the limit is in the form $\infty / \infty$. Take a look at the procedure below -

$\lim_{x \to \infty} x^4e^{-x^3} = \lim_{x \to \infty} \frac{x^4}{e^{x^3}}$,

At this point, one can conclude that the solution should " boil down " to the expression $4 / \infty$, and thus the solution is 0.

Hope that helps!