Question: Question 1 (8 Marks) Let f(x) = e - COSx sin x - 2x (a) Convert f(x) into a form that avoids loss of significance

Question 1 (8 Marks) Let f(x) = e - COSx sin x - 2x (a) Convert f(x) into a form that avoids loss of significance by using the first two nonzero terms of the Taylor series expansion. Denotes it as g(x) . [4.5 marks] (b) Approximate the values of f(0.01) and g(0.01) using four-digit rounding arithmetic. [2 marks] (c) Taking 0.9900002 as the actual value of f(0.01), which approximated value in (b) is better? Explain your answer. [1.5 marks]

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