Let $f ( x , y ) = \left\{ \begin{array} { c c } \frac { \sin ( x - y ) } { x - y } & x \neq y \\1 & x = y\end{array} \right.$

Multiple Choice

Let $f ( x , y ) = \left\{ \begin{array} { c c } \frac { \sin ( x - y ) } { x - y } & x \neq y \\1 & x = y\end{array} \right.$ . Then f is

A) Continuous at (2,2)
B) Discontinuous at (2,2) because f is undefined at (2,2)
C) Discontinuous at (2,2) because the limit of f at (2,2) does not exist
D) Discontinuous at (2,2) because the limit of f at (2,2) is different from the function values at (2,2)
E) Discontinuous at (2,2) for a reason that is different from the ones above