Power Series
1.
X
2n (x 1)n
n=0
Solution: The center of the power series is 1, the radius of convergence is 1/2 and the interval of
convergence is (1/2, 3/2).
2.
X
(e)n (x + 2)n
(n + 1)!
n=0
Solution:
Improper Integrals
Determine whether each of the following integrals converge. If they converge, determine what they
converge to.
1.
Z
x+1
dx
x3 x
2
Solution: To solve the integral you will likely ne
Polar Coordinates
1. Express (1, 1) in polar coordinates. Then write down another representation of the same point,
but with a different value of . Then write down another representation of the same p