Lesson: Maclaurin Series AP Calculus BC

Mathematics

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

Video

13:18

Sample Question Videos

  • 07:16
  • 04:44
  • 03:18

Worksheet

Q1:

Consider the function 𝑓(𝑥)=𝑒.

Find 𝑓(𝑥).

Find 𝑓(𝑥)(), where 𝑓() represents the 𝑛th 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)=𝑥sin.

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

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

Hence, derive the Maclaurin series for sin𝑥.

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

Q3:

Consider the function 𝑓(𝑥)=𝑥cos.

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

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

Hence, derive the Maclaurin series for cos𝑥.

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