Education Technology

Calculus: Taylor Polynomial Examples
by Texas Instruments

Published on August 31, 2011

Objectives

  • Produce various graphs of Taylor polynomials
  • Discover how the accuracy of a Taylor polynomial is associated with the degree of the Taylor polynomial
  • Visualize the accuracy and relate this to symmetry, arc length, and a point of discontinuity
  • Examine certain common functions and draw specific conclusions about the Taylor polynomial associated with these functions

Vocabulary

  • Taylor polynomial
  • degree n
  • accuracy of the approximation
  • neighborhood of a

About the Lesson

This lesson involves Taylor polynomials associated with five common functions. As a result, students will:

  • Learn about Taylor polynomials graphically and numerically.
  • Conjecture about factors that affect the accuracy of Taylor polynomial approximations.
  • Visualize the effects of n and a on the accuracy of the approximation.