Prove that the limit as x->inifinity [x^2 - 2x] / [x^3 - 5] = 0
The general procedure that we have to use to come up with this proof is:
"For all epsilon>0, there exists some N>0, such that for all x, if x>N then this implies that
| [[x^2 - 2x] / [x^3 - 5] - 0] | < epsilon".
N and epsilon are just variables.
The Attempt at a Solution
I simplified the "| [[x^2 - 2x] / [x^3 - 5] - 0] |" down to
"| [[x^2 - 2x] / [x^3 - 5] |"
I'm allowed to manipulate this equation as long as it is preserved. Also I can make helper assumptions as to the value of "N" as long as I account for them in my proof.
I've spent hours staring at this question but I cant figure out how to proceed from here
Any help would be greatly appreciated!