Could someone help me with an Epsilon-delta proof please?

[Meddle]

Hi guys,
I have some problems proving Epsilon-Delta as x approaches infinity questions. Here's the one:

lim x->infinity (x^2 - 2x) / (x^3 -5) = 0

How do I pick N? I'm totally confused now with the ones are proved with delta.

 

[BigGlenntheHeavy]

\(\displaystyle Note: \ \lim_{x\to\infty}\frac{x^2-2x}{x^3-5} \ = \ \lim_{x\to\infty}\frac{x^2}{x^3} \ = \ \lim_{x\to\infty}\frac{1}{x} \ = \ 0\)

\(\displaystyle Now, \ can \ you \ take \ it \ from \ here?\)

 

[galactus]

Here is a 'made up' example close to yours I will use as an example.

\(\displaystyle \lim_{x\to {\infty}}\frac{1}{x-1}=0\)

\(\displaystyle x>N\)

\(\displaystyle N=\frac{1+{\epsilon}}{\epsilon}=1+\frac{1}{\epsilon}\)

\(\displaystyle x>\frac{1}{\epsilon}+1\)

\(\displaystyle x-1>\frac{1}{\epsilon}\)

\(\displaystyle \frac{1}{x-1}<{\epsilon}\)

Now, close it up?.