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Home  >  Volume 32 (Nov. 2015)

An Obscure Theorem of Binmore and a Popular Characterization of Differentiability by Sunday Oluyemi (pages 83-90)
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We present an obscure theorem of K.G. Binmore found in [3] and employ it to give an analytic  proof, the only one known to the author so far, of a popular characterization of differentiation that is an old as Isaac Newton. The hich is as old as Isaac Newton. The age long geometric proof given by George E. Andrews in [1] that this characterization is geometrically evident can now be dispensed with by teachers and students of Elementary Real Analysis.

Keywords: Limit, continuity, differentiability.2010 Amer. Math. Soc. Subject Classification 26 Real Functions