Tufts University
Bluebook No.
Math 13
Final Examination
May 8, 2006
(100 points)
8:30 a.m. – 10:30 a.m.
Instructions:
Write your bluebook number in the space above. No calculators, notes or books are
allowed. Except for the TrueFalse questions, you should show all your work in order to receive full
credit. Simplify your answers. Please box your answers and cross out any work you do not want
graded.
Remember to sign your blue book, indicating that you have neither given nor received
assistance on this exam.
Write your answers to the TrueFalse questions on the inside front cover
of your blue book. Write
T
if the statement is always true, and write
F
otherwise.
1. (12 points)
True or False.
(a) If
S
is the surface of a cube oriented outward and
F
(
x, y, z
) =
(
z, x, y
)
, then
integraldisplayintegraldisplay
S
F
·
d
S
= 0
.
(b) There exists a vector field
F
(
x, y, z
) such that curl
F
=
(
x
2
, z, y
)
.
(c) The angle between the vectors
(
1
,
0
,
1
)
and
(
0
,
1
,
1
)
is
π/
6.
(d) The graph of the quadric surface
x
2
+ 2
y
2
=
z
2
−
1 has only one sheet.
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 Fall '07
 Weiss
 Math, Vector Calculus, blue book, Vector field, Stokes' theorem

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