How can the function
f: ℝ² → ℝ : (x,y) |--> {{x^2+y^2-(x^3y^3)}\over{x^2+y^2}} if (x,y) ≠ (0,0)
be defined in the origin so that we get a continuous function?When I take 'x=y' (so (y,y)) and 'y=x' (so (x,x)) I get:
{{2-y^4}\over{2}}
and
{{2-x^4}\over{2}}
So for the first one I get '1'...