tandfonline.com – Taylor’s theorem part II: advice for socially responsible advertisers
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tandfonline.com har udgivet en rapport under søgningen “Teacher Education Mathematics”: Link til kilde
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tandfonline.com – Poisson’s fundamental theorem of calculus via Taylor’s formula
tandfonline.com har udgivet en rapport under søgningen “Teacher Education Mathematics”: ABSTRACT Formulae display:?Mathematical formulae have been encoded as MathML and are displayed in this HTML version using MathJax in order to improve their display. Uncheck the box to turn MathJax off. This feature requires Javascript. Click on a formula to zoom. ABSTRACT We use Taylor’s formula with Lagrange remainder to make a modern adaptation of Poisson’s proof of a version of the fundamental theorem of calculus in the case when the integral is defined by Euler sums, that is Riemann sums with left endpoints which are equally spaced. We discuss potential benefits for such an approach in basic calculus courses. Link til kilde
tandfonline.com – Arc length of function graphs via Taylor’s formula
tandfonline.com har udgivet en rapport under søgningen “Teacher Education Mathematics”: Abstract Formulae display:?Mathematical formulae have been encoded as MathML and are displayed in this HTML version using MathJax in order to improve their display. Uncheck the box to turn MathJax off. This feature requires Javascript. Click on a formula to zoom. 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… Continue Reading