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

  • 04:46
  • 02:35
  • 09:01

Worksheet

Q1:

Consider the function 𝑓(π‘₯)=𝑒.

Find 𝑓(π‘₯).

Find 𝑓(π‘₯)(), where 𝑓() represents the 𝑛th derivative of 𝑓 with respect to π‘₯.

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(π‘₯)=π‘₯sin.

What are the first four derivatives of 𝑓 with respect to π‘₯?

Write the general form for the 𝑛th derivative of 𝑓 with respect to π‘₯.

Hence, derive the Maclaurin series for sinπ‘₯.

What is the radius 𝑅 of convergence of the Maclaurin series for sinπ‘₯?

Q3:

Consider the function 𝑓(π‘₯)=π‘₯cos.

What are the first four derivatives of 𝑓 with respect to π‘₯?

Write the general form for the 𝑛th derivative of 𝑓 with respect to π‘₯.

Hence, derive the Maclaurin series for cosπ‘₯.

What is the radius 𝑅 of convergence of the Maclaurin series for cosπ‘₯?
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