Find $$\lim_{(x,y) \rightarrow (0,0)} f(x,y)=\lim_{(x,y) \rightarrow (0,0)} \frac{x+y}{x^{2}+y^{2}}$$
I think this limit isn't exist, but I don't know how to prove. I don't know if I prove $\lim_{(x,y) \rightarrow (0,0)} f(x,y) = \infty$ in 1 particular axis ( Ex: Approaching (0,0) along the line y=x ) is enough to conclude that $\lim_{(x,y) \rightarrow (0,0)} f(x,y)$ isn't exist?
Thank u guys so much