(5) Define f: R² → R by
f(xy) = xy/x² + y² if (x, y) = (0,0),
0 if(x,y) = (0,0).
(a) Show that and exists at all points (including the origin) and show that these are not continuous functions.
(b) Is f continuous at the origin? Explain your answer.
(c) Does f have directional derivatives at the origin? Explain your answer.