Epsilon Delta Proof? I always have trouble with understanding the intuition/process of $\epsilon$-$\delta$ proofs.  Could anyone assist me with understanding the solution to the following:
Show that $f$ is continuous at $(0,0)$.
$$f(x,y) =\begin{cases} \dfrac{x^4}{x^2+y^2}&\text{ for }(x,y)\neq (0,0)\\0&\text{ for }(x,y)  = (0,0)\end{cases}$$ 

$$\left|\frac{x^4}{x^2+y^2}\right|=\left|x^2\cdot\frac{x^2}{x^2+y^2}\right|\leq |x|^2\leq x^2+y^2=||(x,y)||^2$$
So, suppose we are given $\epsilon>0$. We need to give $\delta$ such that if $||(x,y)||<\delta$ then $\left|\frac{x^4}{x^2+y^2}\right|<\epsilon$.
What about $\delta=\sqrt{\epsilon}$?
