In this lesson on Taylor's Theorem, we learn about the convergence of Taylor series to f(x) and the importance of Taylor polynomials in providing local approximations of f(x) near x0. We are also introduced to the remainder term and Lagrange's formula for the remainder, which allow us to estimate the error in the approximation of f(x) by a Taylor polynomial. The integral form of the remainder and the proof of its generalization are also discussed. Overall, this lesson provides a comprehensive understanding of Taylor's Theorem and its applications in mathematics.
Taylor polynomials and the remainder term. Convergence of Taylor series to f(x).
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.