# Math Help - Definition of Limit

1. ## Definition of Limit

There's a similar post on this, but I can't understand it and it seems flawed. So I'll try this one.
How do you prove that the lim (as x approaches a) of x^2=a^2?

2. Are you familiar with the delta-epsilon defintion of a limit? I don't want to go into it if it's not what you're looking for.

3. Yes I am.

4. Here's a good site that proves $\lim_{x \to 1}x^2+3=4$ It uses the same method so unless you want I won't type it all out.

http://www.math.ucdavis.edu/~kouba/C...l#SOLUTION%204

5. Thank you. Very helpful.

6. Ok. So the only thing I don't get now as how it works for something like the example I had where the limit equals a variable (also the number the limit is approaching is a variable). I'm having trouble making the connection from the problem I had to ones with real numbers.

How do you show abs(x^2-a^2) is less than epsilon?