Let , , and denote the degree , , and Maclaurin polynomials for , respectively. Which…

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Let

P_2(x)

P_4(x)

, and

P_6(x)

denote the degree

2

4

, and

6

Maclaurin polynomials for

\sin x

, respectively. Which of the following lists these polynomials in order of increasing absolute error when they are used to approximate

\sin(0.5)

? (a)

P_2,\;P_4,\;P_6

(b)

P_4,\;P_6,\;P_2

(c)

P_6,\;P_4,\;P_2

(d)

P_4,\;P_2,\;P_6