Let $f(x,y)$ is provided as follows:
$f(x,y)=\frac{x^2y}{x^2+y^2}$
What i think in this problem is that since $0<\frac {x^2}{x^2+y^2}\leq1$ and consequently the given function is $0<\frac{x^2|y|}{x^2+y^2}\leq |y|$. Hence, the function should be bounded. Is my reasoning incorrect? But the answer is that the function is unbounded, what am I doing wrong?.