Answer
The limit is
$$\lim_{(x,y)\to(2,1)}(2x^2+y)=9.$$
The function is continuous on the whole doman.
Work Step by Step
The limit can be found by the simple substitution:
$$\lim_{(x,y)\to(2,1)}(2x^2+y)=2\cdot2^2+1=9.$$
The function is continuous on the whole domain because for every ordered pair $(x_0,y_0)$
$$\lim_{(x,y)\to(x_0,y_0)}(2x^2+y) = 2x_0^2+y_0.$$