Let $f(x,y) = {\frac{x^2+y^2}{x+y}}$ if $x\neq -y$ and $f(x,y) = 0$ otherwise.
How can I compute $\displaystyle\lim_{(x,y)\rightarrow (0,0)}f(x,y)$ without using polar coordinates tranformation? That is, using only the $\epsilon-\delta$ definitions or else some other algebraic trick?