Question: Task 1: Finite difference approximations [6 marks]Consider the following finite difference approximation of the derivative f' (z) of an appropriately smooth function f (z), with

Task 1: Finite difference approximations [6 marks]Consider the following finite difference approximation of the derivative f' (z) of an appropriately smooth function f (z), with a step size x > 0:f'(z) D(z) = 2 (af(z - z) + a2f(z) + asf(z + Az))where 0 is known.1.a [3 marks]Show that the only possible values of a1, a2, a3 which guarantee second-order accuracy for D(z) are given by1=-3=28 2=0

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