Calculus: Taylor Polynomial Examples

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.