- #1

Maddie1609

- 81

- 11

## Homework Statement

Use the ε-δ definition of limits to prove that lim

_{x→2}x

^{2}= 4.

## The Attempt at a Solution

|x

^{2}- 4| < ε

0 < |x - 2| < δ

|x - 2| |x + 2| < ε

And that's where I get stuck, can I divide both sides by |x + 2| to yield

|x - 2| < ε/|x + 2| = δ

In which case, where do I go from there? Can I input 2 to get ε/4 = δ?