Tea Time Numerical Analysis · Problem 1.2.6

Preliminaries — Leon Brin

Mathematics — Numerical Analysis · taylor-polynomials

Problem

Find the second Taylor Polynomial for

f(x) = \csc x

expanded about

x_0 = \frac{\pi}{4}

. Here are some facts you may find useful:

f'(x) = -\csc(x)\cot(x) \qquad \csc(x) = \frac{1}{\sin(x)}

f''(x) = \csc(x)(1 + 2\cot^2(x)) \qquad \cot(x) = \frac{\cos(x)}{\sin(x)}