Hey everyone, long time lurker first time poster. Unfortunately my first post is a request for help!

Before you ask, yes I've read the sticky on this topic :P However, this is a multi-variable question and I'm really struggling with it. I have to prove this limit using the definition:

I know the definition and inequalities I have to work with:

epsilon > 0, delta > 0

0 < sqrt(x^2 + y^2) < delta

| f(x) - 0 | < epsilon (1)

I've attempted to play around with the equation (1), however it seems that I get a delta that is extremely complex. Is there some simplification that I'm overlooking? I noticed, from the sticky, that I can't have delta in terms of x or y. How can I get passed this?

Thank you very much (I like this emoticon)