1. Consider the following function, f(x) = 0 - far sin (1) if x 0 if...

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1. Consider the following function, f(x) = 0 - far sin (1) if x 0 if x = 0 (a) (3 marks) Prove that the function f is differentiable at x = 0 using the definition of derivatives. (b) (2 marks) Find the formula of the derivative, f'(x) for x 0, using any differentiation rules you have learned in this course. Indicate clearly which rules are used in your computation. 1. Consider the following function, f(x) = 0 - far sin (1) if x 0 if x = 0 (a) (3 marks) Prove that the function f is differentiable at x = 0 using the definition of derivatives. (b) (2 marks) Find the formula of the derivative, f'(x) for x 0, using any differentiation rules you have learned in this course. Indicate clearly which rules are used in your computation.