Recall that lim sin ( ) does not exist, lim x sin ( ) = 0, and lim x2 sin () = 0. x-+0 x-+0 Thus if we define the functions f and g by f (x) = x sin (for x # 0, f(0 = 0, g(x) = x2 sin ( for x * 0, and g(0) = 0, then f and g are continuous at 0. (You may use all of these facts without needing to write out proofs of them.) (a Show that f is not differentiable at 0. (b) Show that g'(0) = 0