Arc length of function graphs via Taylor's formula

• Patrik Nystedt ^[1]
  1. [1] University West

     University West

     Suecia

     
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 52, Nº. 2, 2021, págs. 310-323
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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 1 + (f )2 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.