Computing $\lim_{(x,y)\to (0,0)}\frac{x+y}{\sqrt{x^2+y^2}}$
What is the result of $\lim_{(x,y)\to (0,0)}\frac{x+y}{\sqrt{x^2+y^2}}$ . I tried to do couple of algebraic manipulations, but I didn't reach to any conclusion.
Thanks a lot.
If $$x=r\cos\theta$$ $$y=r\sin\theta$$ then we have $$\text{lim}_{r\rightarrow 0}\frac{r\cos\theta+r\sin\theta}{r} =\cos\theta+\sin\theta=\sqrt{2}\sin(\theta+\frac{\pi}{4})$$ which depends on the angle of approach to the origin.