Tufts University
Math 13
Department of Mathematics
April 10, 2006
Exam 3 (100 points)
noon – 1:20 p.m.
Except in the truefalse questions, show all your work. Simplify and box your answers. No
calculators, notes, or books are allowed. You are required to sign your bluebook. With your
signature you are pledging that you have neither given nor received assistance on the exam.
Students found violating this pledge will receive an F in the course.
1. (10 points) For each statement, write True if it is always true and False if it is not always
true. Write your answers on the inside front cover
of the bluebook. No explanation is
necessary.
a) Let
D
be the plane region bounded on the left by
x
2
+
y
2
= 4 and on the right
by the
y
axis. The integral
integraltextintegraltext
D
x
2
y
+
x
3
y
5
dA
= 0 by symmetry.
b) Let
E
be the solid bounded above by
z
= 4 and below by
z
=
x
2
+
y
2
. The triple
integral
integraltextintegraltextintegraltext
E
(cos
x
)
y
2
z dV
= 0 by symmetry.
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 Fall '07
 Weiss
 Math, Coordinate system, Polar coordinate system

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