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## Homework Statement

Prove that the limit as x->inifinity [x^2 - 2x] / [x^3 - 5] = 0

## Homework Equations

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 can't figure out how to proceed from here

Any help would be greatly appreciated!