For , the third-degree Taylor polynomial about is used to approximate . Given that…

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

For

f(x)=\sin x

, the third-degree Taylor polynomial about

x=0

is used to approximate

f(0.2)

. Given that

|f^{(4)}(z)|\le 1

for all real

z

, calculate a numerical upper bound for the absolute error of this approximation.