Below you will find most of the answers to the practice exam problems. However you should only look at this after you have done the problems.
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Selected answers and hints from the practice exam problems:
2. Answer: 0
3a. Answer: -4/3
3b. Answer: -7/60
4a. Answer: 10
5a. Answer: The region is the xy-plane with the y-axis removed. The curl is undefined when x=0.
5b. Hint: Use the fundamental theorem of line integrals.
6a. Answer: curl(F)=-sin(x)k, div(F)=cos(x) + 2z, (where k is the standard unit vector)
6b. Answer: curl(F)=0, div(F)=0, f=xz+y^2z-(1/3)z^3
8a. Hint: it looks like a spiral staircase type thing.
9. Answer: 36pi
10a. Answer: 713/180
10b. Answer: 0
11. Answer: -6pi
12. Answer: 2pi
14. Answer: 1/3
15. Answer: -2pi
16. Answer: -1/2
17a. Answer: 3pi
17b. Answer: 13pi/20