Math 13
Exam 2
March 12, 2007
Calculus III
(100 points)
Noon–1:20 p.m.
Please do all nine problems below. Except for the truefalse questions, you must show your work
and justify your answers in order for partial or full credit to be awarded.
No books, notes or
calculators are allowed during this exam.
You are required to sign each examination blue book
that you are handing in. With your signature, you are pledging that you have neither given nor
received any help pertaining to this exam. If you are found in violation of this policy, you will be
refered to the Dean of Students and automatically receive an
F
for the course.
1. (6 pts) On the inside cover of your blue book mark the following questions
T
(for
True
) or
F
(for
False
).
NO PARTIAL CREDIT
.
a) For the function
z
=
f
(
x, y
), if
∂f/∂x
(
x
0
, y
0
) = 0 and
∂f/∂y
(
x
0
, y
0
) = 0, then
f
must
have a local maximum or a local minimum at (
x
0
, y
0
).
b) The double integral
integraltextintegraltext
D
f
(
x, y
)
dx dy
in rectangular coordinates is equal to
integraltextintegraltext
D
f
(
r
cos
θ, r
sin
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 Fall '07
 Weiss
 Calculus, 6 pts, 10 pts, 10pts, dx dy

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