Thread: How to prove that this limit does exists...

How can I correctly justify, demonstrate, and properly determine that this limit exists?

lim (x,y) --> (0,0)

Originally Posted by HypatiaDaVinci

How can I correctly justify, demonstrate, and properly determine that this limit exists?
lim (x,y) --> (0,0)

The distance .

So

Thank you very much for the answer. How do you get to the conclusion that I mean... how do you directly relate them?

Originally Posted by HypatiaDaVinci

Thank you very much for the answer. How do you get to the conclusion that I mean... how do you directly relate them?

To prove this by the definition, you should state that
"For all x,y in R, for all epsilon > 0, there exists a delta > 0 such that [d(x, y) < delta] implies [sqrt(x^2 + y^2) < epsilon]
since "d(x, y)" and "sqrt(x^2 + y^2)" are the same thing, you can choose delta to be the epsilon that is given.

Thank you very much, I think I got it now