APPM 2350 Exam 3, Wednesday, November 19 Fall 2008
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On the front of your bluebook, write: (1) your name, (2) your recitation session number, and draw
a grading table, as shown in the margin to the right. Apart from for Problem 1 (for which you
should give only the answers), you must show all your work in your blue book, and BOX your
final answers (A correct answer with no relevant work shown might not receive any credit, while
an incorrect answer with some correct work might receive partial credit). With the exception of a
1 sheet (2 page) handwritten crib sheet, no text book, notes, or calculators are permitted. Please
start each new problem on a new page of the bluebook.
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1. (24 points) In this multiple choice problem, assume that all unspecified functions are continuously
differentiable. For each of the statements below, select option A, B, C, or D:
a. The value of is
¶−1
1¶−1−x2
1−x2¶−1−x2−y2
1−x2−y2
dzdy dx
A. B. C. D.
24
36
Hint: The problem can be solved quickly without working out the triple integrals.
b. The center of mass of a uniform density half-circle is located how far (in terms of the radius) from
the object's straight edge?
A. B. C. D.
1
22
34
3
4
c. The Taylor approximation around the origin to a function of three variables, up to and
f(x,y,z)
including linear terms, contains (at most) how many terms?
A. 2 B. 3 C. 4 D. 5
d. What object is described by the spherical coordinate relation , ?
=cos#0[#[
2
A. A plane B. A circle C. A sphere D. None of the above.
e. The formulas to convert from spherical to cylindrical coordinates are
A. B. C. D. None of the above.
r=sin#
=
z=cos#
r=cos#
=
z=sin#
r=sin#cos
=sin#sin
z=cos#
f. One of the following expressions for the work integral is NOT correct. Identify which one that is.
A. B. C. D.
¶F$Tds ¶F$dr ¶F$nds ¶F$dr
dt dt
g. The volume of a pyramid can be expressed in terms of its base area A and its height h as
A. B. C. D.
V=Ah V=1
2Ah V =1
3Ah V =1
4Ah
h. The vector field becomes conservative if we choose as
F= (z+y)i+xj+g(x,y,z)kg(x,y,z)
A. B. C. 2 D.
x+y x2x+sin2z
Please turn over ⇒
1
2
3
4
T
