Tea Time Numerical Analysis · Problem 1.2.28

Preliminaries — Leon Brin

Mathematics — Numerical Analysis · taylor-remainder

Problem

Suppose

f(x)

is such that

-3 \leq f^{(10)}(x) \leq 7

for all

x \in [0, 10]

. Find lower and upper bounds on the absolute error in using

T_9(x)

expanded about

x_0 = 3

to approximate ((a))

f(0)

. ((b))

f(10)