Fall 2012 Math 152 Group Activity 9 (Review for Exam II) Section ________ Names ____________________ Calculators are not allowed. Problems: 1. Compute . 2. Calculate . 3. Compute . 4. Compute the arc length of the curve given by the parametric equations √
27 from , a. b. 13
0 to 6. 1 c. d. 6 e. 5. Which of the following integrals gives the surface area obtained by rotating the curve for 0
1, about the ‐axis? a. 2
√1
1
d. 16
16
2
b. √1
16
1
e. c. 16
2
, 1
6. Which of the following series diverges by the Test for Divergence? a. ∑
b. ∑
sin
c. ∑
d. ∑
!
sin
e. The Test for Divergence is inconclusive for all of the above series. 7. The recursive sequence defined by 8. Find the sum of the series: ∑
9. If the th partial sum of the series ∑
(a) Find 2, cos
5
cos
converges. Find the limit. . is given by . (b) Find the sum of the series ∑
. 10. Determine whether this sequence converges, and if it does, what it converges to. Clearly explain your reasoning. ln 2
1
ln 3
4
Solutions: 1. ________________________________________ 2. ________________________________________ 3. ________________________________________ 4. ________________________________________ 5. ________________________________________ 6. ________________________________________ 7. ________________________________________ 8. ________________________________________ 9. ________________________________________ 10. _______________________________________