For centered at

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

Problem

For

f(x)=\sin x

centered at

a=0

, approximate

f(0.5)

with a degree-

n

Maclaurin polynomial. Knowing that

|f^{(n+1)}(c)|\le1

for all real

c

, determine the smallest integer

n

that ensures the absolute error does not exceed

1.0\times10^{-4}