Multivariable Limit

karens

1. 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

2. Homework 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.

Related Calculus and Beyond Homework Help News on Phys.org

Coto

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

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

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving