Question

??

Answer 1

I got infinity but its looking for a number.

Answer 2

Just to clarify, you're asking to evaluate\[\lim_{x\rightarrow\infty}\frac{e^{8x}-8x-1}{x^2}\]

Answer 3

Yes

Answer 4

You're definitely right then...this limit definitely goes to infinity. There are several ways to show this, but easiest way is L'Hopital's Rule.\[\lim_{x\rightarrow\infty}\frac{e^{8x}-8x-1}{x^2}=\lim_{x\rightarrow\infty}\frac{8e^{8x}-8}{2x}=\lim_{x\rightarrow\infty}32e^{8x}=\infty\]

Answer 5

So theres no numerical answer you can get for that?

Answer 6

Because it says a numerical answer is expected.

Answer 7

Nope, this limit doesn't "converge" to any numerical answer. It just grows infinitely. That also makes sense because the function \(e^{8x}\) in the numerator grows WAY faster than \(x^2\) in the denominator, so the limit would never approach a finite number.

Answer 8

Alright thank you so much!!

Answer 9

No problem. :)