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

• Mar 20th 2010, 11:40 PM
MatHematicalprooF
[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:
http://i43.tinypic.com/2qusoo.png

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 (Rofl) (I like this emoticon)
• Mar 21st 2010, 12:25 AM
chisigma
Try to use polar coordinates, so that is ...

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

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

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$
• Mar 21st 2010, 12:32 AM
MatHematicalprooF
Quote:

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

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

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

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

Thanks for the advice, but I think this one needs to be solved without the use of polar coordinates. Any ideas?
• Mar 22nd 2010, 02:23 AM
MatHematicalprooF
Does noone have even an inkling on this one? Would really help clarify things for me and for the exam.