Question: Question 2 (a) Let f be the function defined on R by f ( x ) = (x4 esin (#), if x # 0. 0,

Question 2 (a) Let f be the function defined on R by f ( x ) = (x4 esin (#), if x # 0. 0, if x =0 Determine whether f is continuous at 0. (7 marks) (b) Let f be the function defined by ax f (x) = [x1' if x #0 b, if x =0 Find all possible values of a, b E R such that f is continuous at 0. Justify your answer. (7 marks) (c) Let f (x) = |x cos x|. Is f differentiable at 0? If yes, determine the value of f' (0). Justify your answer. (6 marks)

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