Barrons AP Calculus - David Bock

31. (a) For f (x) = cos x, f′ (x) = −sin x, f ′′ (x) = −cos x, f ′′′(x) = sin x, f(4) (x) = cos x, f(5) (x) =
    −sin x, f(6) (x) = −cos x. The Taylor polynomial of order 4 about 0 is

Note that the next term of the alternating Maclaurin series for cos x is

(b)

(c) The error in (b), convergent by the Alternating Series Test, is less absolutely than the first term

dropped: