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) (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!