Math 152 In Class Exam 3 Review
Find the sum or show the series is not convergent.
1. 
2. 
3. 
4. 
5. 
6. 
7.
8. 
Test for convergence.
9. 
Also estimate the
remainder, 
.
10. 
11. 
12. 
What is the sum?
Test for convergence and estimate for each convergent
series.
13. 
14. 
15. 
Find a power series and give the radius and interval of convergence for each function.
16. 
17. 
18. 
19. 
20. 
21. 
Find the Taylor series about a and find the radius and interval of convergence for each function.
22. 
, a=4
23. 
, a=2
24. 
, a=0
25. f(x) = cos x , a=0
26. 
, a=0
27. 
, a=0
28. 
Find the nth degree Taylor polynomial about a and estimate 
.
29. f(x) = tan x
, a = 0, n = 3 |x|<π/6
30. f(x) = tan x
, a = 
, n=3 
31. 
, a = 0, n = 6
32. 
, a = 2,
n=6
33. f(x) = sec x a=0, n=2
34. f(x)=sec x a=π/4, n=2
35. Find the distance between the centers of the two
spheres, 
and 
. Do they intersect?