# Help needed with a specific epsilon-delta limit proof

1. Aug 10, 2012

### sergey90

1. The problem statement, all variables and given/known data

limit[1/(x-2)^3]=-inf as x->2

2. Relevant equations

3. The attempt at a solution
2-delta<x<2 1/(x-2)^3 < M
-delta<x-2<0 (x-2)^3>1/M
(-delta)^3<(x-2)^3<0

=>(-delta)^3=1/M=>-delta=croot(1/M)=>delta=-croot(1/M) ....huh? how could delta be negative?

2. Aug 11, 2012

### micromass

Staff Emeritus
I have no idea what you just did.

What are these three equations?? What is M??

3. Aug 11, 2012

### sergey90

its the epsilon delta proof for infinite limits. Its just how they are proved generally. M is any negative number

4. Aug 11, 2012

### micromass

Staff Emeritus
I still have no idea what you did, sorry. I can see delta's and M's and stuff, but I have no idea what you're doing.

Can you write in words what you're doing between every step? Write what you want to prove. Just write some text to guide the reader.

Also, if M is negative, then $-\sqrt[3]{1/M}$ is positive...

5. Aug 11, 2012

### Zondrina

You want to prove :

$lim_{x→2} \frac{1}{(x-2)^3} = -∞$

So you want to use this statement :

$\forall$M>0, $\exists$δ>0 | 0 < |x-2| < δ $\Rightarrow$ f(x) < M

Start with f(x) < M and massage it to find a suitable δ.