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

Meddle

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Jun 2, 2010
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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.
 
Note: limxx22xx35 = limxx2x3 = limx1x = 0\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

Now, can you take it from here?\displaystyle Now, \ can \ you \ take \ it \ from \ here?
 
Here is a 'made up' example close to yours I will use as an example.

limx1x1=0\displaystyle \lim_{x\to {\infty}}\frac{1}{x-1}=0

x>N\displaystyle x>N

N=1+ϵϵ=1+1ϵ\displaystyle N=\frac{1+{\epsilon}}{\epsilon}=1+\frac{1}{\epsilon}

x>1ϵ+1\displaystyle x>\frac{1}{\epsilon}+1

x1>1ϵ\displaystyle x-1>\frac{1}{\epsilon}

1x1<ϵ\displaystyle \frac{1}{x-1}<{\epsilon}

Now, close it up?.
 
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