Barrons AP Calculus - David Bock

38. (C) The Maclaurin expansion is

The Lagrange remainder R, after n terms, for some c in the interval |x| 2, is

Since R is greatest when c = 2, n needs to satisfy the inequality

Using a calculator to evaluate successively at various integral values of x gives

y(8) > 0.01, y(9) > 0.002, y(10) < 3.8 × 10 −4 < 0.0004. Thus we achieve the desired

accuracy with a Taylor polynomial at 0 of degree at least 10.