Consider on the domain

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

Problem

Consider

g(x)=\sqrt{1+x}

on the domain

x>-1

. Let

Q_2(x)=1+\dfrac{x}{2}-\dfrac{x^2}{8}

be its 2nd–degree Maclaurin polynomial. Determine the largest interval

[0,r]

(r>0)

on which the error of using

Q_2(x)

to approximate

g(x)

is less than

0.0001

. (a)

0\le x\le 0.08

(b)

0\le x\le 0.18

(c)

0\le x\le 0.10

(d)

0\le x\le 0.13