$$ f(x,y) = \begin{cases} \dfrac{2x^4y - 5x^2y^2+y^5}{(x^2+y^2)^2}, & \text{if $(x,y) \neq (0,0)$} \\ 0 & \text{if $(x,y) = (0,0)$} \end{cases}$$
I know this function to be discontinuous by putting $y=mx$, but i need help to prove the discontinuity using $\epsilon-\delta$ form, where i know that if a function is discontinuous then there $\exists \epsilon $ such that $\forall \delta \gt 0, |x-0|\lt \delta \Rightarrow |f(x,y) - f(0,0)| \gt \epsilon$.