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 work in your blue book in order to receive a full credit.
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 + y 2 and above by the plane 2x + z = 3, in the o
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 function g(x, y ) = x4 2xy + y 2 .
2
We have the partial
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 + 3z = 6. For the Lagrange multipliers, we then have the
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 equations for the line containing the edge P Q:
A directio
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 receive full credit. Simplify your answers as much as
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 shown in Figures 1 and 2. (You dont need to justify
your
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 to receive full credit. Simplify your answers as much a
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 work to receive full credit. Simplify your answers as mu
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 to the point (3, 0, 2), as well as the direction
vecto
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, 1, 0 and a direction vector for
the line is also 0, 1,
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
jadler.math.tufts.edu/courses/math13/resources.html
on Thu
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 work to receive full credit. Simplify your answers as muc
Tufts University
Department of Mathematics
Final Examination
Math 13
December 16, 2009
8:3010:30 a.m.
Instructions: Please do all problems below. You must show your work and justify your answers
in order for partial or full credit to be awarded. No books
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 partial or full credit to be awarded. No books, notes or ca
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 ending at the point
(2, 3, 5).
(b) the ellipse x2 /a2 + y
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
allowed. Except for the TrueFalse questions, you should
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 T if the statement is always true, and write F otherwis
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 receive full credit. Simplify your answers as much as
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 all your work in your
blue book in order to receive ful
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 full credit. A correct answer with no work may not nece
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 trueflse questioDs,show all yoru work. Sirnplify yoru qJrswers.No calculs,tors, notes, or books are
Math 13
Tufts University Department of Mathematics Exam 3 (100 points)
April 10, 2006 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 requi
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Math 13
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 are allowed. Except for the TrueFalse questions, yo
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Math 13 Calculus III
Exam 2 (100 points)
March 12, 2007 Noon1:20 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 bo
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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, explain, simplify, and box all your answers. Except for