The 3rd–degree Maclaurin polynomial for is

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

Problem

The 3rd–degree Maclaurin polynomial for

f(x)=e^{2x}

P_3(x)=1+2x+2x^2+\dfrac{4}{3}x^3

. Determine the largest symmetric interval centered at

0

on which

P_3(x)

approximates

f(x)

with an error not exceeding

0.001

. (a)

[-0.20,0.20]

(b)

[-0.16,0.16]

(c)

[-0.18,0.18]

(d)

[-0.12,0.12]