For the Maclaurin series

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

Problem

\sin x = x-\dfrac{x^{3}}{3!}+\dfrac{x^{5}}{5!}-\dfrac{x^{7}}{7!}+\cdots

, let

P_{n}(x)

denote the polynomial obtained by keeping all terms up to and including

x^{2n+1}

. What is the smallest integer

n

for which

|\sin x - P_{n}(x)|<10^{-5}

for every

x

[-1,1]

? (a)

n=2

(b)

n=5

(c)

n=3

(d)

n=4