The Maclaurin polynomial of degree is used to approximate for

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

Problem

The Maclaurin polynomial of degree

n

is used to approximate

\ln(1+x)

for

0\le x\le 0.2

. What is the least integer

n

that guarantees the error is less than

10^{-6}

throughout this interval? (a)

n=6

(b)

n=7

(c)

n=5

(d)

n=8