Question

L'hospital's Rule: Other forms! help! lim as (x^3)(e^-x^2) approaches infinity

Answer 1

\[\lim_{x \rightarrow \infty} x^{3} e^{-x^{2}}\]

Answer 2

I know that I have to take the derivative, but I don't know where to go from there. This really confuses me

Answer 3

The expression is equivalent to x^3 /e^(x^2) which goes to zero as the denominator tends to infinity , so you have a small number over a a number moving towards to infinity...so thats zero

Answer 4

You dont need L'Hopitals Rule here, see my explanation above.

Answer 5

does the nominator go to zero?

Answer 6

No, as x gets larger, x^3 gets large. But what I am saying, is that e^(x^2) runs to infinity faster than x^3 does

Answer 7

okay. I understand now! thank you!

Answer 8

Welcome. As a note, even if the numerator was x^250, the answer is still zero, becuase e^(x^2) runs to infinity faster than x^ a power