# Limit homework issue

1. Jul 12, 2012

### azizlwl

1. The problem statement, all variables and given/known data
If f(x)=x2 prove that $$\lim_{x \to 2} f(x)= 4$$
Solution given:
We must show that given any ε >0, find δ >0 such that |x2-4|<ε when 0<|x-2|<δ

Choose δ≤1 so that <|x-2|<1
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Confuse between the word 'find' and 'choose'.

2. Jul 12, 2012

### LCKurtz

Re: Limits

$|x^2-4|=|(x+2)(x-2)|=|x+2|\cdot |x-2|$. So if $|x-2|<1$ how big can $|x+2|$ be? Then once you figure that out, how much smaller than 1 does $|x-2|$ need to be to make the whole thing less that $\epsilon$?

3. Jul 13, 2012

### HallsofIvy

Re: Limits

You can "find" many values of $\delta$ that will work and then "choose" one of those. That is the same as "finding" a value.

4. Jul 13, 2012

### azizlwl

Re: Limits

Thanks. My confusion must be interpreting the word "find" as calculate in usual mathematics or physcis problems.

Last edited: Jul 13, 2012