13) [16 marks, 8 marks for part a), 4 marks for each of the other parts] a) Let f(x) = x sin() if x * 0 0 if x = 0 i) Find f'(x) for all x * 0. [2 marks] ii) Use the Squeeze Theorem and the definition of the derivative to show how that f(x) is differentiable at x = 0 and to find the value of f'(0). [2 marks] iii ) Find lim f'(Xn) where an = V27n' [2 marks] iv) Is f'(x) continuous at x = 0? Briefly explain your answer. [2 marks] b) Let g(x) be such that | g(x) | M for all x E [-1, 1]. Let h(x) = 3 x2g(x) if x * 0 0 if x = 0 Use the Squeeze Theorem to show that h(x) is differentiable at x = 0 and find h'(0). c) Find an example of a function F(x) defined on all of R such that F(x) is differentiable at x =0 but not at any other point. (Hint: You have come across such a function already in this course.)