Proving Multivariable Limit: f(x, y) → 0

[karens]

Homework Statement

Consider that f(x, y) = [sin^2(x − y)] / [|x| + |y|].
Using this, prove: lim(x,y)→(0,0) f(x, y) = 0

Homework Equations

Definition of a limit, etc.

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.

 

[Coto]

Start with the definition of a limit:

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

One way to think of it is to start by fixing epsilon and then finding what delta must be (in terms of epsilon).