Limit of function of several variable

[violette]

Homework Statement

lim(x,y)->(0,0) x²y / 2x³-y³

Homework Equations

The Attempt at a Solution

I found lim f(x,0)=0 and lim f(0,y)=0.So i assume limit exists and equals 0?
I would like to get some tips on how to solve this type of problems?Do I always find f(x,0) and f(0,y)?Because I always seem to get 0 as the answer when I do that.

Thanks in advance =)

 

[Dick]

Try taking the limit along the line x=y. There are more than two ways for (x,y) to approach (0,0).

 

[violette]

hi thanks!
means I can try any ways in hope that one way will prove that limit does not exist?
how can i prove that limit exist then?
thanks =)

 

[I like Serena]

Hi violette!

To proof it exists, you need an epsilon-delta proof (see the definition of a limit).

It's easier to proof it does not exist.
For that you need a path that yields a different limit.
Can you find such a path that may cause trouble?

Here's a nice example that may be of help:
http://en.wikipedia.org/wiki/Multivariable_calculus#Limits_and_continuity