Taylor Polynomial Teacher Resources

In this calculus worksheet, students apply the Taylor Series to exponential functions based at either zero or one. There are 2 questions with multiple parts.

In this math learning exercise, students graph the function f(x) = sinx on a set of axes that is at least half the size of a page of notebook paper.

In this calculus learning exercise, students solve various functions for the Taylor Series using a variety of solving methods including the double angle formula, partial fractions, and u substitution. There are 8 questions.

For this calculus worksheet, students find the Taylor series for each function adn give the interval where the series converges. The two page worksheet contains nine questions. Answers are not included.

Learners analyze geometric series in detail. They determine convergence and sum of geometric series, identify a series that satisfies the alternating series test and utilize a graphing handheld to approximate the sum of a series.

In this linear approximation worksheet, students determine the derivative of a function and explore properties of the error when using a tangent line to approximate a function graph. This two-page worksheet contains four problems.

In this math worksheet, students Find the interval of convergence of the power series. Special attention should be paid by checking the endpoints.

In this center of mass worksheet, learners determine the center of mass of an isosceles triangle. They examine functions and determine the tangent error bound.  This one-page worksheet contains 5 problems.

Students learn to define a Taylor polynomial approximation to a function f of degree n about a point x = a. They also learn to graph convergence of Taylor polynomials. They use Taylor polynomials to approximate function values.

Video lesson showing the formula for a Taylor series expansion to five terms and uses it to approximate the cosine function. Includes the graphs of a specific number of terms of the approximate function using a graphing calculator. [18:05]

Video first reviews the formula for a Taylor series expansion and then defines the error function to be the difference between the polynomial approximation and the actual function. Properties of the derivatives of the error function are...

This lesson details the taylor series with a general description, formulas, and an explanation of its usage in mathematics. Content also includes a focus on the Taylor series as limits of Taylor polynomials, including two examples.

Video uses a property of the error function for a Taylor series expansion from the previous video to bound the (n+1)th derivative of the error function. Result is the Lagrange error bound. [15:08]

Video uses a property of the error function for a Taylor series expansion from a previous video to bound the (n+1)th derivative of the error function. Result is the Lagrange error bound.

Video shows how to calculate the Lagrange error bound for a Taylor series polynomial approximation. [11:52]

In this activity, the students will learn the use of Taylor's polynomials to integrate functions that are not easily integrated by hand. They learn this by completing a series of calculations that vary from integrating to finding a...

Lagrange error bound for Taylor Polynomial approximation.

Multiplying two Taylor polynomials.

Lagrange error bound for Taylor Polynomial approximation.

Approximating a function at 0 using a polynomial

Understanding the properties of the remainder or error function for an Nth degree Taylor approximation of a function

Rationale for Euler's Formula and Euler's Identity

Learn about the Lagrange remainder with this helpful reference tool. Provides a detailed definition and examples that enhance further explanation. Includes links to related topics.

The exercise explores first-, second-, and third-degree polynomial approximations. Students label the graphs of the polynomial approximations. The handout is available in PDF format.