Let be the function g(x)= 1 3+2x for real numbers near .

MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Let

g

be the function

g(x)=\frac{1}{3+2x}

for real numbers

x

near

0

. (1) Obtain a Maclaurin series for

g(x)

and write the first three non-zero terms. (2) Using the series from part (a), compute

g'(0)

without differentiating the closed-form expression for

g

. Show your work.