On the Remainder in Taylor’s Theorem
Fotios C. Paliogiannis · College Mathematics Journal · 2024
SummaryThe problem of approximating any n + 1 times differentiable function near a particular point by a polynomial of degree ≤n is of great importance both in theory and in applications of analysis. In its various formulations, this problem has a long and interesting history, going back almost 300 years. As is well known, Taylor’s Theorem tells us one way that such an approximation can be made and gives an expression for the error in the approximation. The purpose of this article is to give an overview of Taylor’s Theorem and explore interconnections among various expressions for the remainder term.