# Homework Help: Multivariable Limit

1. Jun 7, 2010

### karens

1. The problem statement, all variables and given/known data
Consider that f(x, y) = [sin^2(x − y)] / [|x| + |y|].
Using this, prove: lim(x,y)→(0,0) f(x, y) = 0

2. Relevant equations

Definition of a limit, etc.

3. The attempt at a solution
I don't know how to start... I've been trying to self-teach limits for a while and Don't know how to do it with the absolute values and two variables. Help is much needed.

2. Jun 7, 2010

### Coto

$$\forall \epsilon > 0\ \ \ \exists \delta > 0$$ such that $$||f(x,y) - f(x_0,y_0)|| < \epsilon$$ whenever $$||(x,y) - (x_0,y_0)|| < \delta$$.