The function $f$ is defined as
$$f(x, y) =\frac{x^2 y^2} {x^2 y^2 +|x-y|}$$ for $(x,y)\neq(0,0)$ and $0$ otherwise.
We can clearly take two different paths $y=x$ and $y=-x$ which would give two different limits and thus $f$ is not continuous at $(0,0)$. How would introducing polar coordinates lead to such a result exactly?