The Taylor series for centered at can be written as for

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

Problem

The Taylor series for

h(x)=\ln x

centered at

x=2

can be written as

h(x)=\sum_{n=0}^{\infty} b_n (x-2)^n

for

|x-2|<2

. What is the value of

b_3

? (a)

-\dfrac{1}{24}

(b)

\dfrac{1}{12}

(c)

\dfrac{1}{24}

(d)

\dfrac{1}{4}