# Worksheet: Taylor Series

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

**Q3: **

Consider the function .

Find the Taylor series representation of the function at .

- A
- B
- C
- D
- E

Are the terms of the Taylor series representation for the function finite or infinite?

- AFinite
- BInfinite

**Q5: **

For a function : , and for . Find the Taylor series expansion of at .

- A
- B
- C
- D
- E

**Q7: **

What is the necessary and sufficient condition for the function to have a Taylor series representation about ?

- A is not equal to for any positive integer . ( is the derivative of .)
- B exists.
- C is not equal to 0.
- D is not equal to 0 for any positive integer . ( is the derivative of .)
- E exists for any positive integer . ( is the derivative of .)

**Q8: **

Consider the function .

Find the Taylor series representation of about .

- A
- B
- C
- D
- E

Find the interval of convergence of the Taylor series representation of about .

- A
- B
- C
- D
- E

What is the radius of convergence of the Taylor series representation of about ?

- A2
- B
- C0
- D
- E1

**Q11: **

Find the Taylor series of the function about .

- A
- B
- C
- D
- E

**Q12: **

Write the first four terms of the Taylor series expansion of in ascending powers of .

- A
- B
- C
- D
- E

**Q13: **

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

- A
- B
- C
- D
- E

**Q14: **

Find the radius of convergence for the Taylor series of about .

- A
- B1
- C
- D
- E

**Q15: **

Find the radius of convergence for the Taylor series of about .

- A
- B
- C2
- D
- E