Tea Time Numerical Analysis · Problem 1.2.12

Preliminaries — Leon Brin

Mathematics — Numerical Analysis · taylor-remainder

Problem

Find

\xi(x)

as guaranteed by Taylor's theorem in the following situation. ((a))

f(x) = \cos(x)

x_0 = 0

n = 3

x = \pi

. ((b))

f(x) = e^x

x_0 = 0

n = 3

x = \ln 4

. ((c))

f(x) = \ln(x)

x_0 = 1

n = 4

x = 2