Determine constant c so that g(x,y) is continuous at every point $$g(x,y)=\begin{cases} \frac{x^3+xy^2+2x^2+2y^2}{x^2+y^2} & \text{if} & (x,y) \neq (0,0) \\
c & \text{if} & (x,y) = (0,0) \end{cases}$$
Should I set the first function equal to c and then solve using polar coordinates?

For $(x,y) \neq (0,0)$, with some simplifications we may get:
$$g(x,y)=x+2$$
In order for the function to be continuous  at the origin, $g(0,0)$ must exist and we must have that $\lim_{x \to (0,0)} g(x,y)=g(0,0)$.
When is that the case? 

 When $c=g(0,0)=\lim_{(x,y) \to (0,0)} g(x,y)=2$

