(a) Let the function f(T) = sinh be approximated by an interpolating polynomial of degree 14 using 15 nodes equally spac

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A Let The Function F T Sinh Be Approximated By An Interpolating Polynomial Of Degree 14 Using 15 Nodes Equally Spac 1 (15.45 KiB) Viewed 24 times

(a) Let the function f(T) = sinh be approximated by an interpolating polynomial of degree 14 using 15 nodes equally spaced in the interval (-1,1]. What upper bound can be placed on the absolute error? (4 marks) (b) () Derive the approximation L'O 4f(h) – 3f(0) - f(2h) and establish its error term. 2h (ii) Use the result of part (i) to approximate f'(o) if f(2)=rcos 1. Take h = 0.001. (3+2=5 marks)