Partial Differentiation Ex 2.2 Eng Mathematics by H.K. Das Test for continuity when
$f(x,y) = \frac{x^3\,y^3}{x^3+y^3}$ when $x\neq0, y\neq0$ and f(x,y)=0 when $x=0,y=0$. 

for $$x>0,y>0$$ we have $$x^3+y^3\geq 2(xy)^{3/2}$$ thus we obtain
$$\frac{x^3y^3}{x^3+y^3}\le \frac{x^3y^3}{2(xy)^{3/2}}=\frac{1}{2}(xy)^{3/2}->0$$
