# Math Help - Continuity Problem

1. ## Continuity Problem

I don't know how to do this question;

Define the function f: R -> R by

f(x)= { x^2 x>= 0
{ 0 x < 0

Prove that f is continous.

2. Originally Posted by Sterwine
I don't know how to do this question;

Define the function f: R -> R by

f(x)= { x^2 x>= 0
{ 0 x < 0

Prove that f is continous.
1. show that $f(0)$ is defined.

2. show that $\lim_{x \to 0} f(x)$ exists by comparing the one-sided limits from the left and the right of x = 0.

3. show that $\lim_{x \to 0} f(x) = f(0)$