Overview
Earlier we studied linear and quadratic approximations. If we continue to improve our approximations by using the third, fourth, fifth, ... derivatives the result is a power series. These power series are called Taylor's series. This session gives a formula describing the terms of a Taylor's series and a few examples of its application.
Lecture Video and Notes
Video Excerpts
» Clip 1: Introduction to Taylor's Series (00:07:00)
From Lecture 38 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Introduction to Taylor's Series
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» Clip 3: Taylor's Formula Examples (00:04:00)
From Lecture 38 of 18.01 Single Variable Calculus, Fall 2006
Recitation Video
Finding Taylor's Series
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Taylor's Series of a Polynomial
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Worked Example
Proving That the Taylor Series of a Function is Equal to the Function