Multi-variable limit using epsilon-delta technique

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Hi guys, I'm new to this forum, I am a mechanical engineering student, I am actually taking Multi-variable Calculus (Calculus III, on my college) this semester and I'm having a lot of trouble proving the limit of a multivariable equation using the epsilon-delta technique.

Example:

lim (3xy^2)/(x^2+y^2) x->(0,0)

I don't even understand what is about, I look the limit of the equation along x and y axis y=mx and y=x^2 and found L=0 but how do I prove it is really 0.
The book show something about epsilo-delta technique but say's nothing about how using this technique, it look kind of random.

Thanks a lot Link-

PS. Sorry for my english, im not a good english speaker or writter but at always I do my best :biggrin:
 

Answers and Replies

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Homework Helper
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The easiest way to do this problem is to rewrite the function in polar coordinates. Then it should be easy to see that as r->0, the function goes to zero.
 
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The easiest way to do this problem is to rewrite the function in polar coordinates. Then it should be easy to see that as r->0, the function goes to zero.
Thanks a lot.
 

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