cosx-e Let f(x)=- sin x (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). (b) Approximate the...

Extracted text: cosx-e Let f(x)=- sin x (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). (b) Approximate the values of f(0.01) and g(0.01) using four-digit rounding arithmetic. (c) Taking 0.990033 as the actual value of f(0.01), which approximated value in (b) is better? Explain your answer.