# 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

Q2:

Consider .

Find the Maclaurin series of .

• A
• B
• C
• D
• E

Use the first three terms of this series to find an approximate value of to 2 decimal places.

Q3:

The function can be represented by the power series . Use the first two terms of this series to find an approximate value of to two decimal places.

Q4:

The function can be represented by the power series . Use the first two terms of this series to find an approximate value of to 2 decimal places.

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

Q6:

Find the Maclaurin series of .

• A
• B
• C
• D
• E

Q7:

Use the Maclaurin series of to express as an infinite series.

• A
• B
• C
• D
• E

Q8:

Use the Maclaurin series of to express as an infinite series.

• A
• B
• C
• D
• E

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