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 for
- C for
- D
- 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

**Q4: **

Find the Maclaurin series of .

- A
- B
- C
- D
- E