Limit of $$\lim_{(x,y)\rightarrow(0,0)}\frac{\sin(2x+2y)-2x-2y}{\root\of {{x^2+y^2}}}$$
How can evaluate this limit?
I tried using polar coordinates like $x=r\cos\theta$ and $y=r\sin\theta$. put the thing in the sin doesn't turn into something neat.
Also i tried evaluating along different paths. But I don't know how that helps.
Edit: Also could you prove that the limit you found is the actual limit using the $\epsilon - \delta$ method.
Thanks!