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.
Wait! Did you really do the problems yet?
Selected answers and hints from the practice exam problems:
1a. Answer: -4/3
1b. Answer: -7/60
2a. Answer: 10
3a. Answer: The region is the xy-plane with the y-axis removed. The curl is undefined when x=0.
3b. Hint: Use the fundamental theorem of line integrals.
4a. Answer: curl(F)=-sin(x)k, div(F)=cos(x) + 2z, (where k is the standard unit vector)
4b. Answer: curl(F)=0, div(F)=0, f=xz+y^2z-(1/3)z^3
6a. Hint: it looks like a spiral staircase type thing.
7. Answer: 36pi
8a. Answer: 713/180
8b. Answer: 0
9. Answer: -6pi
10. Answer: 2pi
12. Answer: 1/3
13. Answer: -2pi
14. Answer: -1/2
15a. Answer: 3pi
15b. Answer: 13pi/20