6) Consider the function _1- cos(3x) S(x) =- 9x a) Explain why this way of computing the function Ax) is problematic if x is near certain values. What are these problematic values? b) Use the trigonometric identity, sin’ u: 1-cos(2u) - to obtain another form of f(x) less prone to error. c) Find an approximation for f(x), called g(x), that is less prone to error by finding the first 3 nonzero terms of a power series for f(x), using the Maclaurin series, •(-1)* x* - (2k)! cos.x = (Recall that a Maclaurin series is a Taylor series centered at 0.) d) Compute lim- 1-cos(3x) 9x using L'Hôpital's rule on this original form of the function. Then, compute lim g(x) (the approximation you found in part (c)), and compare your results.

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