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Arc length of function graphs via Taylor’s formula
University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0001-6594-7041
2020 (English)In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211Article in journal (Refereed) Epub ahead of print
Abstract [en]

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. As a means for generating interesting examples of exact arc length calculations in calculus courses, we recall two large classes of functions f with the property that (Formula presented.) has a primitive, including classical examples by Neile, van Heuraet and Fermat, as well as more recent ones induced by Pythagorean triples of functions. We also discuss potential benefits for our proposed definition of arc length in introductory calculus courses. © 2020, © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

Place, publisher, year, edition, pages
2020.
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Mathematical Analysis
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URN: urn:nbn:se:hv:diva-15157DOI: 10.1080/0020739X.2020.1751320Scopus ID: 2-s2.0-85083643127OAI: oai:DiVA.org:hv-15157DiVA, id: diva2:1427932
Available from: 2020-05-04 Created: 2020-05-04 Last updated: 2020-05-04

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Nystedt, Patrik

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