Prove a limit using the delta epsilon method

**msokol89** · March 4th 2011, 09:32 AM

Hello,
How can I prove that the limit of the following function equals to zero, using the delta epsilon method?
$\lim_{x\rightarrow 2}(x^2-4)=0$

I have reached this step, but I do not know what to do next:
$|x-2|< \frac{\varepsilon}{|x+2|}$

thanks in advance, Michael

**Plato** · March 4th 2011, 09:56 AM

Originally Posted by msokol89

Hello,
How can I prove that the limit of the following function equals to zero, using the delta epsilon method?
$\lim_{x\rightarrow 2}(x^2-4)=0$
I have reached this step, but I do not know what to do next:
$|x-2|< \frac{\varepsilon}{|x+2|}$