Arc length of function graphs via Taylor's formula
History and Overview
2019-04-16 v1
Abstract
We use Taylor's formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subdivisions which are equally spaced. We discuss potential benefits for such an approach in introductory calculus courses.
Cite
@article{arxiv.1904.07006,
title = {Arc length of function graphs via Taylor's formula},
author = {Patrik Nystedt},
journal= {arXiv preprint arXiv:1904.07006},
year = {2019}
}