# Lesson Worksheet: Maclaurin and Taylor Series of Common Functions Mathematics • Higher Education

In this worksheet, we will practice finding the Taylor/Maclaurin series representation of common functions such as exponential and trigonometric functions and binomial expansion.

**Q1: **

Consider .

Find a power series representation for .

- A
- B
- C
- D
- E

Find its interval of convergence.

- A
- B
- C
- D
- E

**Q5: **

Consider the binomial expansion for .

Which of the following expressions is its fourth term?

- A
- B
- C
- D
- E

What is the limit of the th term as tends to infinity?

- A
- B
- C
- D
- E1

Hence, write in summation (or sigma) notation a series which is equal to the limit of as tends to infinity.

- A
- B
- C

What is the value of this series?

- A
- B
- C
- D

**Q9: **

Find the Maclaurin series of .

- A
- B
- C
- D
- E

**Q10: **

Write the first three terms of the Taylor expansion for about in ascending powers of .

- A
- B
- C
- D
- E