Chapter Eleven: Applications of Series

Question 1

What is the Maclaurin series of e^x? What is this series’ interval of convergence?

Answer 1

(-∞, ∞)

Question 2

What is the Maclaurin series of sinx? What is this series’ interval of convergence?

Answer 2

(-∞, ∞)

Question 3

What is the Maclaurin series of cosx? What is this series’ interval of convergence?

Answer 3

note: it is the same as sine, but with just n instead of n+1 in the a_n expression

(-∞, ∞)

Question 4

What is the Maclaurin series of 1 ÷ (1-x) ? What is this series’ interval of convergence?

Answer 4

(-1, 1)

Question 5

What is the Maclaurin series of arctanx? What is this series’ interval of convergence?

Answer 5

note: it is the same as sinx, but without the factorial in the bottom

[-1, 1]

Question 6

What is the Maclaurin series of ln(1 + x)? What is this series’ interval of convergence?

Answer 6

(-1, 1]

Question 7

What is the derivative of the power series?

Answer 7

Question 8

What is the integral of the power series?

Answer 8