Could someone help me solve this using L'Hopital rule? I end up getting infinity/infinity which equals infinity but that's not the right asnwer.
That's correct. The limit of denominator and numerator are both infinity, so you have and can apply L'Hopital's rule. Taking the derivative of numerator and denominator gives and again you have . So apply L'Hopital's rule again to get . Since this goes to infinity as x goes to infinity, you can conclude that .
You probably didn't mean to say this in your first post, but I should point out that you can't assume that is infinity - it might be, but it could also be any positive number or zero.