Chapter Eleven: Applications of Series Flashcards
What is the Maclaurin series of ex? What is this series’ interval of convergence?
(-∞, ∞)
What is the Maclaurin series of sinx? What is this series’ interval of convergence?
(-∞, ∞)
What is the Maclaurin series of cosx? What is this series’ interval of convergence?
note: it is the same as sine, but with just n instead of n+1 in the an expression
(-∞, ∞)
What is the Maclaurin series of 1 ÷ (1-x) ? What is this series’ interval of convergence?
(-1, 1)
What is the Maclaurin series of arctanx? What is this series’ interval of convergence?
note: it is the same as sinx, but without the factorial in the bottom
[-1, 1]
What is the Maclaurin series of ln(1 + x)? What is this series’ interval of convergence?
(-1, 1]
What is the derivative of the power series?
What is the integral of the power series?