What is the Epsilon-Delta Proof for Continuity?

[Mattofix]

Homework Statement

i have a couple of questions to anser and they start 'Give epsilon - delta proofs that the following functions are continuous at the indicated points.'

im guessing its not going to be too hard but what is the name of this epsilon - delta proof so i can search for and learn about it.

The Attempt at a Solution

 

[SNOOTCHIEBOOCHEE]

It is just one of the definitions of Continuity.

A fuction f is continuous at Xo if

For each $$\epsilon > 0$$ there exists $$\delta$$ such that

|X-Xo|<$$\delta$$ Implies |f(X)-f(Xo)|<$$\epsilon$$

For all X,Xo belonging to Domain of f