# Worksheet: Maclaurin Series

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

**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

**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

**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