Tea Time Numerical Analysis · Problem 1.2.15

Preliminaries — Leon Brin

Mathematics — Numerical Analysis · maclaurin-polynomial

Problem

Let

f(x) = e^x

. ((a)) Find the

n^{th}

Maclaurin polynomial

P_n(x)

for

f(x)

. ((b)) Find a bound on the error in using

P_4(2)

to approximate

f(2)

. ((c)) How many terms of the Maclaurin polynomial would you need to use in order to approximate

f(2)

to within

10^{-10}

? In other words, for what

n

does

P_n(2)

have an error bound less than or equal to

10^{-10}