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f: ℝ² → ℝ : (x,y) |--> [tex]{{x^2+y^2-(x^3y^3)}\over{x^2+y^2}}[/tex] 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:

[tex]{{2-y^4}\over{2}}[/tex]

and

[tex]{{2-x^4}\over{2}}[/tex]

So for the first one I get '1' when y=0

and for the second one I get '1' when x=0

So can I say that if (x,y)=0 --> f=1 ??

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# Continuous extension

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