Exercise 7
1. Determine whether the alternating series converges
2. Use the ratio test for absolute convergence to determine whether the series converges or
diverges.
a.
b.
3. Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4, and then find the nth
Maclaurin polynomials for the func- tion in sigma notation.
a. eax
b. cos px
4. Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = x0, and then find the
nth Taylor polynomial for the function in sigma notation.
a. 1/x; x0 = -1
b. sin px; x0 = 1/2