13. Let a, b be real numbers and f: R R be a function defined by...

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13. Let a, b be real numbers and f: R R be a function defined by 3+a1-3r f(x) = if x < 0 X 1+btan (1) if x 0. Assume that f(x) is continuous at x = 0. (a) Determine the value of a and justify your computation. (b) If we further assume that f is differentiable at 0, determine the value of b and justify your answer. 13. Let a, b be real numbers and f: R R be a function defined by 3+a1-3r f(x) = if x < 0 X 1+btan (1) if x 0. Assume that f(x) is continuous at x = 0. (a) Determine the value of a and justify your computation. (b) If we further assume that f is differentiable at 0, determine the value of b and justify your answer.