Education Technology

Taylor Polynomials Exploration

Subject Area
Math: Calculus: Series and Taylor Polynomials
Math: AP Calculus: AP Calculus
Level
9-12
Activity Time
50 Minutes
Software
TI-Nspire™ CX
TI-Nspire™ CX CAS
TI Calculator
TI-Nspire™ CX series
TI-Nspire™ CX CAS/CX II CAS
TI-Nspire Version
5.0
Resource Types
Lessons
Format
TNS

Taylor Polynomials Exploration

Activity Overview

In this activity, students will examine another kind of polynomial approximation that is a generalization of the tangent line approximation. These polynomials are called Taylor polynomials.

Objectives

Students will:

  • Define a Taylor polynomial approximation to a function f of degree n about a point x = a.
  • Graph convergence of Taylor polynomials.
  • Use Taylor polynomials to approximate function values.

Vocabulary

  • Taylor polynomial
  • factorial
  • derivatives

About the Lesson

Taylor polynomial approximations are introduced as generalizations of tangent line approximations. The graphing handheld is used as a tool to graph Taylor polynomial approximations of functions. Taylor polynomials are also used to approximate specific function values. In this activity, students will examine another kind of polynomial approximation that is a generalization of the tangent line approximation. These polynomials are called Taylor polynomials.

Subject Area
Math: Calculus: Series and Taylor Polynomials
Math: AP Calculus: AP Calculus
Level
9-12
Activity Time
50 Minutes
Software
TI-Nspire™ CX
TI-Nspire™ CX CAS
TI Calculator
TI-Nspire™ CX series
TI-Nspire™ CX CAS/CX II CAS
TI-Nspire Version
5.0
Resource Types
Lessons
Format
TNS
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