Chapter 1.2, Problem 13ES

Let

$f(x)=\frac{x\cos x-\sin x}{x-\sin x}.$

1. a. Find lim_x→0 f(x).
2. b. Use four-digit rounding arithmetic to evaluate f(0.1).
3. c. Replace each trigonometric function with its third Maclaurin polynomial and repeat part (b).
4. d. The actual value is f(0.1) = −1.99899998. Find the relative error for the values obtained in parts (b) and (c).