Lesson: Taylor Series Mathematics • Higher Education

In this lesson, we will learn how to find Taylor series of a function and find the radius of convergence of the series.

Lesson Plan

Students will be able to

find the Taylor series of a function and the radius of convergence of the series.

Q1:

The following table shows the value of function and some of its derivatives at .

Write the first 5 terms of the Taylor series of .

Q2:

Consider the function .

Find the Taylor series representation of the function at .

Are the terms of the Taylor series representation for the function finite or infinite?

Q3:

Consider the function .

Find the Taylor series expansion of at .

Write the Taylor series expansion of in sigma notation.