Math 13
Tufts University
Department of Mathematics
Final Exam
May 9, 2011
No calculators, cell phones, iPods, notes, scratch paper or books are allowed. Except for
Problem 1, you must show all your wo
Math 13 Solutions to Exam 3 Review Spring 2007 1. Set up (but do not evaluate) a triple integral in the order indicated for the volume of the solid E if (a) E is bounded below by the paraboloid z = x2
Math 13
Tufts University
Department of Mathematics
Exam 2 Solutions
November 15, 2010
1. (15 points) Find and classify (as local minima, local maxima, or saddle points) all critical
1
points of the fu
Solutions for Math 13 Exam 2, Fall 2009
November 23, 2009
1. The volume of such a box is V (x, y, z ) = xyz , so we look to maximize V (x, y, z ) subject to the constraint
that g (x, y, z ) = x + 2y +
Math 13
Tufts University
Department of Mathematics
Exam 1 Solutions
October 11, 2010
1. (15 points): Consider the triangle whose vertices are
P (1, 2, 0)
Q(2, 1, 2)
R(4, 2, 1).
(a) Give parametric equ
Tufts University
Department of Mathematics
Final Exam
Math 13
May 10, 2010
8:30 to 10:30 am
Instructions: No calculators, notes or books are allowed. Unless otherwise stated, you must show
all work to
Math 13
Tufts University
Department of Mathematics
Exam 2 Solutions
April 11, 2011
1. (5 points) Using symmetry, determine if the following integrals are positive, negative, or zero for the regions sh
Tufts University
Department of Mathematics
Exam 2
Math 13
April 5, 2010
12:00 noon to 1:20 pm
Instructions: No calculators, notes or books are allowed. Unless otherwise stated, you must show
all work
Tufts University
Department of Mathematics
Exam 1
Math 13
February 22, 2010
12:00 noon to 1:20 pm
Instructions: No calculators, notes or books are allowed. Unless otherwise stated, you must show
all w
Tufts University
Department of Mathematics
Solutions to Final
Math 13
Spring 2009
1. True or False?
(a) F: cylinder
(b) T
(c) F
(d) F: maybe
saddle
(e) T
2. (a) The vector < 3, 0, 2 >, from the origin
Math 13, Exam 1 Solutions
1. (a) False the dot product of two vectors is a scalar. In this case, i j = 0.
(b) False this is a hyperboloid of two sheets.
(c) True a normal direction for the plane is 0,
Math 13
Final Exam Review
Spring 2012
No calculators should be used in these problems. Simplify your answers as much as possible and
box your answers. Model solutions will be posted on the website
jad
Tufts University
Department of Mathematics
Final Exam
Math 13
December 16, 2011
8:30 to 10:30 am
Instructions: No calculators, notes or books are allowed. Unless otherwise stated, you must show
all wo
Tufts University
Department of Mathematics
Final Examination
Math 13
December 16, 2009
8:30-10:30 a.m.
Instructions: Please do all problems below. You must show your work and justify your answers
in o
Tufts University
Department of Mathematics
Math 13
Final Examination Fall 2009: Solutions
Instructions: Please do all problems below. You must show your work and justify your answers
in order for part
Tufts University
Department of Mathematics
Solutions to Final Exam Review
Math 13
Spring 2012
1. Parameterize the following curves.
(a) the line segment in space starting at the point (6, 1, 0) and en
Math 13
Tufts University
Final Examination
(100 points)
Bluebook No.
May 4, 2009
8:30 a.m. 10:30 a.m.
Instructions: Write your bluebook number in the space above. No calculators, notes or books are
al
Math 13
Tufts University
Department of Mathematics
Final Exam Solutions
May 9, 2011
1. (10 points) True or False. Write your answers to this problem on the inside front cover
of your blue book. Write
Math 13
Tufts University
Department of Mathematics
Final Exam
May 10, 2010
8:30 to 10:30 am
Instructions: No calculators, notes or books are allowed. Unless otherwise stated, you must show
all work to
y
2
1
0
0
1
2
3
4
x
Figure 1: Domain for problem 3
Math 13
Tufts University
Department of Mathematics
Exam 2
November 15, 2010
No calculators, notes, scratch paper or books are allowed. You must show
Math 13
Tufts University
Department of Mathematics
Exam 1
October 11, 2010
No calculators, notes, scratch paper or books are allowed. You must show all your work in your
blue book in order to receive
Math 13
Tfts University Depa.rtmentof Mathematics Exam 2 (100points)
March 13, 2006 noon 1:20p.m.
This exarn consists of 9 problems. Except ir the true-flse questioDs,show all yoru work. Sirnplify
Math 13
Tufts University Department of Mathematics Exam 3 (100 points)
April 10, 2006 noon 1:20 p.m.
Except in the true-false questions, show all your work. Simplify and box your answers. No calcu
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Tufts University Final Examination (100 points)
Bluebook No. May 8, 2006 8:30 a.m. 10:30 a.m.
Instructions: Write your bluebook number in the space above. No calculators, notes or books ar
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Exam 2 (100 points)
March 12, 2007 Noon1:20 p.m.
Please do all nine problems below. Except for the true-false questions, you must show your work and justify your answers in ord
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Math 13
Tufts University Department of Mathematics Exam 1
February 22, 2007
This exam consists of 10 problems which are not necessarily in increasing order of difficulty. Show all your work, explai