Lim epsilon delta

Question

Let $f(x,y)=\frac{x^4+y^4}{x^2+y^2}$, $(x,y)\neq (0,0)$ How to prove that $lim f(x,y)=0$ if $(x,y) \rightarrow (0,0)$ ;use epsilon delta

I can start from that ... $\frac{x^4+y^4}{x^2+y^2} <\frac{x^4+2x^2y^2+y^4}{x^2+y^2}$

Answer 1

$=(x^{2}+y^{2})^{2}/(x^{2}+y^{2})=x^{2}+y^{2}<\delta^{2}=\epsilon$ by choosing $\delta=\sqrt{\epsilon}$.