Dragomir, Sever S (2007) Approximating Real Functions Which Possess n-th Derivatives of Bounded Variation and Applications. Research report collection, 10 (4).

Abstract

The main aim of this paper is to provide an approximation for the function f which possesses continuous derivatives up to the order n−1 (n ≥ 1) and has the n−th derivative of bounded variation, in terms of the chord that connects its end points A = (a, f (a)) and B = (b, f (b)) and some more terms which depend on the values of the k derivatives of the function taken at the end points a and b, where k is between 1 and n. Natural applications for some elementary functions such as the exponential and the logarithmic functions are given as well.

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