Hello everyone, this is my first topic on this forum, so if by chance this question was asked in the past, redirect me to the relevant post.

So, I understand the definition of function limit, I just can't figure how to solve those problems.

For example, I have

$\displaystyle lim(x->2)(x²-4)=5$

So I write |x²-9|<ε, 0<|x-2|<δ

then

|x-3||x+3|<ε

and what's now? I know that probably I should assume that δ<1 or something, and then I stuck.

If there a place when I can see just a big amount of examples, this would be great.

Thank you.