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Lesson: Maclaurin Series

In this lesson, we will learn how to represent exponential and trigonometric functions as power series, find the expansion around zero, and find the interval of the series convergence.

Worksheet • 3 Questions

Q1:

Consider the function .

Find .

  • A
  • B
  • C
  • D
  • E

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

  • A
  • B for
  • C
  • D for
  • E for

Hence, derive the Maclaurin series for .

  • A
  • B
  • C
  • D
  • E

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

  • A
  • B
  • C
  • D
  • EIt does not converge.

Q2:

Consider the function .

What are the first four derivatives of with respect to ?

  • A , , , and
  • B , , , and
  • C , , , and
  • D , , , and
  • E , , , and

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

  • A
  • B
  • C
  • D
  • E

Hence, derive the Maclaurin series for .

  • A
  • B
  • C
  • D
  • E

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

  • A
  • B
  • C
  • D
  • E

Q3:

Consider the function .

What are the first four derivatives of with respect to ?

  • A , , , and
  • B , , , and
  • C , , , and
  • D , , , and
  • E , , , and

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

  • A
  • B
  • C
  • D
  • E

Hence, derive the Maclaurin series for .

  • A
  • B
  • C
  • D
  • E

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

  • A
  • B
  • C
  • D
  • E
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