Oct. 25, 2007
Math 112, Prelim 2
Time: 7.30 -9p.m.
1) Write your name,
your instructor's name,
and the section number on the front cover.
2) Show all your work. A correct answer may get little credit unless the method is correct.
3) Do the problems in any order you like, but label the answers clearly.
4) This is a closed book test. Calculators, notes, or crib sheets are not allowed.
The four problems are worth 25 points each. Parts of the same problem have roughly equal
1) Consider the region R enclosed by the curves
a) Use the slicing method ("washer" shaped slices) to find the volume of the solid obtained by
rotating R around the
b) Use the method of cylindrical shells to find the volume obtained by rotating R around the
2 bonus points if you can explain any obvious relationship between the answers to a) and b).
2) Consider the curve
above the -axis from