Tea Time Numerical Analysis · Problem 1.2.7

Preliminaries — Leon Brin

Mathematics — Numerical Analysis · taylor-remainder

Problem

The hyperbolic sine,

\sinh(x)

, and hyperbolic cosine,

\cosh(x)

, are derivatives of one another. That is,

\frac{d}{dx}(\sinh(x)) = \cosh(x)

and

\frac{d}{dx}(\cosh(x)) = \sinh(x).

Find the remainder term,

R_{43}

, associated with the

43^{rd}

Maclaurin polynomial for

f(x) = \cosh(x)