For centered at

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

Problem

For

f(x)=e^{x}

centered at

a=0

, the value at

x=0.2

is approximated by its degree-

n

Maclaurin polynomial. Given that

|f^{(n+1)}(c)|\le e^{0.2}

for

0\le c\le0.2

, determine the least integer

n

that guarantees the absolute error is less than

1.0\times10^{-6}