Let . A third–degree Taylor polynomial is used to approximate near…

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

Problem

Let

f(x)=\sin x

. A third–degree Taylor polynomial

P_3

is used to approximate

f

near

x=0

. (a) Write

P_3(x)

for

f

centered at

x=0

. Show your work. (b) Using your result from part (a), determine a numerical upper bound for

|f(0.200)-P_3(0.200)|

. Clearly state any values you use to justify your bound.