Lesson: Maclaurin Series

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

Worksheet: 5 Questions

Q1:

Consider the function 𝑓 ( 𝑥 ) = 𝑒 .

Find 𝑓 ( 𝑥 ) .

Find 𝑓 ( 𝑥 ) ( ) , where 𝑓 ( ) represents the 𝑛 th derivative of 𝑓 with respect to 𝑥 .

Hence, derive the Maclaurin series for 𝑒 .

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

Q2:

Consider the function 𝑓 ( 𝑥 ) = 𝑥 s i n .

What are the first four derivatives of 𝑓 with respect to 𝑥 ?

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

Hence, derive the Maclaurin series for s i n 𝑥 .

What is the radius 𝑅 of convergence of the Maclaurin series for s i n 𝑥 ?

Q3:

Consider the function 𝑓 ( 𝑥 ) = 𝑥 c o s .

What are the first four derivatives of 𝑓 with respect to 𝑥 ?

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

Hence, derive the Maclaurin series for c o s 𝑥 .

What is the radius 𝑅 of convergence of the Maclaurin series for c o s 𝑥 ?
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