Question: 1. Compute the first three non-zero terms in the Taylor series for the following functions centred about the specified point a. [5 + 5 =

1. Compute the first three non-zero terms in the Taylor series for the following functions centred about the specified point a. [5 + 5 = 10 marks] (a.) f(x) = In(x2), a =1 (b.) f(x) = tan '(e-x - 1), a =0 2. Calculate the cubic spline functions that pass through the points (0.5, 2), (1, 1), (2, 0.5) and (4, 0.25) with the second derivatives equal to zero at the two endpoints. [12 marks]

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