Math 12
Tufts University Department of Mathematics Exam I
September 22, 2003
No books, notes, or calculators. Cross out what you do not want us to grade. You must give reasons for full credit. You are required to sign your exam book.
1. (10 point
Solutions to Exam III (April 4, 2005) Math 12 Spring 2005 Tufts University (1a). One computes: x -1 -1 1 -1 1 = = = x-2 2-x 2 1 - x/2 2 n=0 2
n
=
-1 n x . 2n+1 n=0
x This geometric series converges to the indicated value provided that < 1; the
Tufts University
Department of Mathematics
Math 12, Test 2
Monday, November 10, 2008
121:20 p.m.
No calculators, notes, scratch paper or books are allowed. Except where indicated, you must show all your work in
your blue book in order to receive full cred
Tufts University
Department of Mathematics
M ath 1 2
October9 ,2007
12:00*1:20
Exam 1
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Tirfts University
N ov 5 , 2 007
D epartmento f M athematics
Math 1 2
Exam I I
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TuftsUniversity
Department f Mathematics
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FinalE xam
M ath1 2
1
December.4,2007
8:30 1 0:30
No books, notes, cell phones, or calculators. The exam has three pages,pleasemake sure you have all of
them. In all problems you must show all your work in the bl
Tufts University
Department of Mathematics
Math 12, Exam I
Monday, October 11, 2010
12:00 p.m.-1:20 p.m.
No calculators, notes, scratch paper or books are allowed. Except where indicated, you must show
all your work in your blue book in order to receive f
Math 12
Tufts University Department of Mathematics Exam 3
November 13, 2006 12:00-1:20
No books, notes or calculators are allowed. Cross out what you do not want us to grade. You must show all your work in order to received full credit. Please wri
Math 12
Tufts University Department of Mathematics Exam 3
November 15, 2004 11:501:20
No books, notes, or calculators. Cross out what you do not want us to grade. You must give reasons for full credit. You are required to sign your exam book. With
Math 12 Exam 3
Tufts University Department of Mathematics
November 14, 2005 12:00-1:20
No books, notes, or calculators. Cross out what you do not want us to grade. You MUST give reasons for full credit. You are required to sign your exam book. Wit
Math 12
Tufts University Department of Mathematics Exam 3 Solutions
8n 3n x . n
1. (a) an =
Therefore, 8n+1 x3(n+1) n n an+1 = lim n 3n = 8|x|3 lim = 8|x|3 . n n n + 1 an n+1 8 x
n=1 1 an converges if 8|x|3 < 1 |x| < 2 . Therefore, the
n
lim
Math 12
Tufts University Department of Mathematics Final Exam
May 7, 2004 8:30-10:30 am
Instructions: Final course grades will be available to you 24 hours after they have been posted on SIS. No calculators, notes or books allowed. Remember to sig
Math 12
Tufts University Department of Mathematics Final Exam
May 5, 2006 8:30-10:30 am
Instructions: Final course grades will be available to you 24 hours after they have been posted on SIS. No calculators, notes or books allowed. Remember to sig
Tufts University
Department of Mathematics
Math 12, Test 1
Monday, October 6, 2008
12:00 p.m.-1:20 p.m.
No calculators, notes, scratch paper or books are allowed. Except where indicated, you must show
all your work in your blue book in order to receive fu