# Worksheet: Maclaurin Series

In this worksheet, we will practice finding Maclaurin series of a function and finding the radius of convergence of the series.

Q1:

Consider the function .

Find .

• A
• B
• C
• D
• E

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

• A
• B
• C for
• 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 ?

• AIt does not converge.
• B
• C
• D
• E

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

Q4:

Find the Maclaurin series of .

• A
• B
• C
• D
• E

Q5:

Consider the function .

Derive the Maclaurin series for .

• A
• B
• C
• D
• E

Using the Maclaurin series, find to 5 decimal places.

Q6:

Find the Maclaurin series of . Write your answer in sigma notation.

• A
• B
• C
• D
• E

Q7:

Find the Maclaurin series of .

• A
• B
• C
• D
• E

Q8:

Find the Maclaurin series of .

• A
• B
• C
• D
• E

Q9:

If the Maclaurin series of the function is , find .

• A
• B
• C
• D
• E5

Q10:

If the Maclaurin series of the function is , find the equation of the tangent to the curve of at .

• A
• B
• C
• D
• E

Q11:

Find the radius of convergence for the Maclaurin series for .

• A
• B
• C
• D1
• E

Q12:

Write the first four nonzero terms of the Maclaurin expansion for in ascending powers of .

• A
• B
• C
• D
• E

Q13:

Find the Maclaurin series for .

• A
• B
• C
• D
• E

Q14:

Find the radius of convergence for the Maclaurin series for .

• A
• B
• C
• D10
• E1

Q15:

By calculating the Maclaurin series for and , or otherwise, find the Maclaurin series for .

• A
• B
• C
• D
• E

Q16:

A Maclaurin series is given by . Find the radius of convergence for the series.

• A
• B
• C2
• D1
• E

Q17:

Find the Maclaurin series of the function .

• A
• B
• C
• D
• E