Let Then F Is

A)Continuous at (0,0)
B)Discontinuous at

Let $f ( x , y ) = \left\{ \begin{array} { c c } \frac { x y } { \sqrt { x ^ { 2 } + y ^ { 2 } } } & ( x , y ) \neq ( 0,0 ) \\0 & ( x , y ) = ( 0,0 ) \end{array} \right.$ . Then f is

A) Continuous at (0,0)
B) Discontinuous at (0,0) because f is undefined at (0,0)
C) Discontinuous at (0,0) because the limit of f at (0,0) does not exist
D) Discontinuous at (0,0) because the limit of f at (0,0) is different from the function values at (0,0)
E) Discontinuous at (0,0) for a reason that is different from the ones above