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# epsilon delta definition of continuity watch

1. We define a function f : R^2 → R by
f(x, y) := ( x^2)/(x^2+y^2) if (x,y) dont equal (0,0)

And f (x,y)=0 if (x,y) = (0, 0).
(a) Prove with the /δ definition that f is continuous at (0, 0).
Any help i know the definition just cant do it getting confused
2. (Original post by omassey)
We define a function f : R^2 → R by
f(x, y) := ( x^2)/(x^2+y^2) if (x,y) dont equal (0,0)

And f (x,y)=0 if (x,y) = (0, 0).
(a) Prove with the /δ definition that f is continuous at (0, 0).
Any help i know the definition just cant do it getting confused
What is the definition? Substitute the definitions in and see what you get.
3. There must be something wrong with what you've posted - f is NOT continuous at (0, 0).
4. (Original post by DFranklin)
There must be something wrong with what you've posted - f is NOT continuous at (0, 0).
PRSOM - in my haste, I squashed the voice of doubt which emerged when noting that y=0 gives a limit of 1…
5. This is the question coppied and pasted is it not continous since at (0,0) f=0
6. (Original post by omassey)
This is the question coppied and pasted is it not continous since at (0,0) f=0
It's not continuous.

Consider the function g(x) = f(x, x).

If f was continuous, g would be too.

But g(x) = 1/2 when x is non-zero, while g(0) = 0.
7. (Original post by omassey)
This is the question coppied and pasted is it not continous since at (0,0) f=0
Are you sure that it wasn't supposed to be away from the origin?
8. (Original post by omassey)
This is the question coppied and pasted is it not continous since at (0,0) f=0
I don't believe it was copied and pasted, since it is phrased ungrammatically. Sorry.
9. It was,my teacher cant speak english well.

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Updated: December 5, 2014
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