Let f(x,y) = 0 if xy ≠ 0 and f(x,y) = 1if xy = 0. (i) Calculate:∂f∂x(0,0) ,∂f∂y(0,0) (ii) Show that f is not continuous at (0, 0).

Let f(x,y) = 0 if xy ≠ 0 and f(x,y) = 1
if xy = 0. (i) Calculate: $\frac{\partial f}{\partial x} (0, 0), \frac{\partial f}{\partial y} (0, 0)$ (ii) Show that f is not continuous at (0, 0).

Match the items on the right to the items on the left.