Lesson: Maclaurin Series Mathematics • Higher Education

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

Lesson Plan

Students will be able to

recall that the Maclaurin series of a function is the special case of the Taylor series where ,
find the Maclaurin series of exponential and trigonometric functions,
find the radius of convergence of a Maclaurin series.

Q1:

Consider the function .

Find .

Find , where represents the th derivative of with respect to .

Hence, derive the Maclaurin series for .

What is the radius of convergence of the Maclaurin series for ?

Q2:

Consider the function .

What are the first four derivatives of with respect to ?

Write the general form for the th derivative of with respect to .

Hence, derive the Maclaurin series for .

What is the radius of convergence of the Maclaurin series for ?

Q3:

Consider the function .

What are the first four derivatives of with respect to ?

Write the general form for the th derivative of with respect to .

Hence, derive the Maclaurin series for .

What is the radius of convergence of the Maclaurin series for ?