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On the Remainder in the Taylor Theorem

by Lior Bary-Soroker (Hebrew University. Israel) and Eli Leher (Hebrew University Israel)

This article originally appeared in:
College Mathematics Journal
November, 2009

Subject classification(s): Calculus | Single Variable Calculus | Series
Applicable Course(s): 3.2 Mainstream Calculus II

An inductive proof is presented for the bounds of the remainder of Taylor expansion. This result, with Darboux's theorem, implies the classical formula for the remainder.

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Capsule Course Topic(s):
One-Variable Calculus | Function Approximation
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