f(x, y)=\left\{\begin{array}{cl} \frac{x y}{x^{2}+y^{2}} & \text { if }(x, y) \neq(0,0) \\ 0 & \text { if }(x, y)=(0,0) \end{array}\right. was in Figure4. (a) Show that fx(0,0) and fy(0,0) exist.

(b) Show that f(x,y) is not continuous at (0,0) (c) Show that fr and fy are not continuous at (0,0).