Answer
The limit is
$$\lim_{(x,y)\to(2,4)}\frac{x+y}{x^2+1}=\frac{6}{5}$$
The function is continuous on its' domain.
Work Step by Step
This limit is calculated by a simple substitution
$$\lim_{(x,y)\to(2,4)}\frac{x+y}{x^2+1}=\frac{2+4}{2^2+1}=\frac{6}{5}.$$
This function is continuous on its domain because for every ordered pair $(x_0,y_0)$ we have
$$\lim_{(x,y)\to(x_0,y_0)}\frac{x+y}{x^2+1}=\frac{x_0+y_0}{x_0^2+1}.$$
