Lesson: Lagrange Error Bound Mathematics • Higher Education

In this lesson, we will learn how to use the Lagrange error bound (Taylor’s theorem with remainder) to find the maximum error when using Taylor polynomial approximations.

Lesson Plan

Students will be able to

use the Lagrange error bound to find the maximum error when using Taylor polynomial approximations,
use the Lagrange error bound to find the number of terms of a Taylor polynomial required to make an approximation to a specified degree of accuracy.

Lesson Video

Lesson Playlist

04:27
04:37
04:03

Lesson Worksheet

Q1:

Find the Lagrange error bound when using the second Taylor polynomial for the function at to approximate the value . Round to five decimal places.

Q2:

Find the Lagrange error bound when using the third Maclaurin polynomial for the function at to approximate the value .

Q3:

Determine the least degree of the Maclaurin polynomials needed to approximate the value of with an error less than 0.001 using the Maclaurin series of .