Suppose forall epsilon > 0  exists delta > 0 forall x 

   0 <|x|<delta -> |f(x)|<epsilon

therefore exists delta > 0 forall x,y

  0 < x^2 + y^2 < delta^2 -> |xy/(x^2+y^2)|< 1/2

therefore

  0 < delta/2 < delta^2 ->  1/2 < 1/2  (letting x = y = delta/4)

therefore

  1/2 < 1/2,

a contradiction[]