Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Series and Taylor Polynomials

9-12

45 Minutes

• ##### Device
• TI-Nspire™ Navigator™
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.0

## Taylor Polynomial Examples

#### Activity Overview

Taylor polynomials associated with five common functions.

#### 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

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.