# Thread: [SOLVED] Proving a multi variable limit (using epsilon-delta)

1. ## [SOLVED] Proving a multi variable limit (using epsilon-delta)

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)

2. Try to use polar coordinates, so that is ...

$x= \rho\cdot \cos \theta$

$y= \rho\cdot \sin \theta$ (1)

Kind regards

$\chi$ $\sigma$

3. Originally Posted by chisigma
Try to use polar coordinates, so that is ...

$x= \rho\cdot \cos \theta$

$y= \rho\cdot \sin \theta$ (1)

Kind regards

$\chi$ $\sigma$
Thanks for the advice, but I think this one needs to be solved without the use of polar coordinates. Any ideas?

4. Does noone have even an inkling on this one? Would really help clarify things for me and for the exam.