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Math 241, Spring 1998, exam 4
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There are 7 problems on 4 pages. Problems 1 and 2 are worth 15 points each. Each
of the other problems is worth 14 points. SHOW your work. CIRCLE your
answer. NO CALCULATORS! CHECK your answer, whenever possible.
1. Find the maximum of f(x, y)=xy on x2+y2=1.
2. Find the absolute extreme points of f(x, y)=x
2+y
2on
{(x, y)|−1≤x≤3,−1≤y≤4}.
3. Find the volume of the solid which is bounded by z=9−x
2−y
2and z=0.
4. Find the area inside r=4sinθand outside r=2.
5. Find the volume of the solid which is bounded by x=0, y=0, z=0,and
x+2y+3z=6.
6. Find the volume of the solid which is bounded by z=p9−x2−y2and
z=px2+y2.
7. Find the volume of the intersection of x2+y2+(z−6)2≤16 and
x2+y2+z2≤16 .