Tea Time Numerical Analysis · Problem 1.2.30

Preliminaries — Leon Brin

Mathematics — Numerical Analysis · taylor-remainder

Problem

Find a theoretical upper bound, as a function of

x

, for the absolute error in using

T_4(x)

to approximate

f(x)

. ((a))

e^x \sin x

;

x_0 = 0

. ((b))

e^{-x^2}

;

x_0 = 0

. ((c))

\frac{10}{x} + \sin(10x)

;

x_0 = \pi