Some Basic Properties of Differentiable Functions

E. Mahmudov ()
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E. Mahmudov: Istanbul Technical University

Chapter Chapter 5 in Single Variable Differential and Integral Calculus, 2013, pp 145-170 from Springer

Abstract: Abstract Rolle’s theorem and the mean value theorems of Lagrange and Cauchy are proved for differentiable functions. Next, Fermat’s theorem concerning relative extreme values is given. Then Taylor’s formula is investigated, and in particular, its remainder term is given in the different forms due to Lagrange, Cauchy, and Peano. Furthermore, it is indicated why sometimes the Taylor series of a function does not converge to that fuction. The Maclaurin series for elementary functions is derived and power series in both real and complex variables are studied. Finally, Euler’s formulas are proved.

Keywords: Power Series; Basic Property; Taylor Series; Differentiable Function; Open Interval (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-91216-86-2_5

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DOI: 10.2991/978-94-91216-86-2_5

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