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Download as PDF; Printable version; In other projects ... Continuity; Rolle's theorem; ... Template:Calculus is used to give a brief outline of calculus topics ...
Template: Calculus topics. 10 languages. ... Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide
Download as PDF; Printable version; In other projects ... Continuity; Rolle's theorem; ... Template:Calculus is used to give a brief outline of calculus topics ...
In these limits, the infinitesimal change is often denoted or .If () is differentiable at , (+) = ′ ().This is the definition of the derivative.All differentiation rules can also be reframed as rules involving limits.
Elementary Calculus: An Infinitesimal Approach; Nonstandard calculus; Infinitesimal; Archimedes' use of infinitesimals; For further developments: see list of real analysis topics, list of complex analysis topics, list of multivariable calculus topics
Recently, Katz & Katz [8] give a positive account of a calculus course based on Keisler's book. O'Donovan also described his experience teaching calculus using infinitesimals. His initial point of view was positive, [9] but later he found pedagogical difficulties with the approach to nonstandard calculus taken by this text and others. [10]
A form of the epsilon–delta definition of continuity was first given by Bernard Bolzano in 1817. Augustin-Louis Cauchy defined continuity of = as follows: an infinitely small increment of the independent variable x always produces an infinitely small change (+) of the dependent variable y (see e.g. Cours d'Analyse, p. 34).
In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point. Derivative tests can also give information about the concavity of a function.
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