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: The center of the power series is 2, but the ratio of
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 need to use partial fractions. The denominator will facto
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 point, but with a
different value of r.
Solution: You pr