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## Homework Statement

Using the epsilon-delta definition, prove that the function f:R[tex]^{2}[/tex] [tex]\rightarrow[/tex] R by f(x,y) = xy/((x[tex]^{2}[/tex]) + (y[tex]^{2}[/tex])), and f(0,0) = 0 is not continuous.

## The Attempt at a Solution

I just really have no clue how to set up a delta-epsilon proof for functions that involve quotients. I went ahead and set up as much delta information as I could, but I have no idea how to set up the epsilon part:

|x-x[tex]_{0}[/tex]|<[tex]\delta[/tex], |y-y[tex]_{0}[/tex]|<[tex]\delta[/tex], and |(x-x[tex]_{0}[/tex])+(y-y[tex]_{0}[/tex])|<[tex]\delta[/tex] (Those are supposed to be x (initial) and y (initial) for the delta info.... I couldn't get LaTex to set them up correctly...)

Can someone give me a couple of good pushes in the right direction? :-)