Tufts University
Department of Mathematics
Exam 1
Math 11
October 6, 2008
No books, notes, or calculators are allowed on the exam. Please do all of your work in
the blue book. Remember to sign your exam book. With your signature, you are pledging
that you
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Review questions for Exam 1, Math 11, Fall
2008
3=
1
4
6. State the denition of the derivative of a function
f (x). Use denition to compute the derivative
the
of f (x) = x2 + 1.
1. Compute the derivative of the following functions.
(a) y = sin(x2
Solutions to review questions for Exam 1, Math 11, Fall 2008
1. (a) y = (2x cos x x2 sin x) cos(x2 cos x)
(b) y = sec2 x etan x ex sec2 ex
1
1
(2x 2x )(3x + 2 x) (x2 x)(3 + x )
2
(c) y =
(3x + 2 x)
(d) y = 22x+1 1 sec( x2 + 1 x) tan( x2 + 1 x)
x2
2
2. (a)
5. Let f (x) be the function with domain [0, 8] whose
Review questions for nal exam, Math 11,
Fall 2008
x
graph in shown, and let g (x) =
1. Evaluate the following indenite integrals.
curved parts of the graph are a quarter circle and
a semicircle.)
1
esi
Solutions to review questions for nal exam, Math 11, Fall 2008
1. (a) Use the substitution u = sin1 x. Then du/dx = 1/ 1 x2 , so
1
esin x
dx =
1 x2
1
eu du = eu + C = esin
x
+ C.
(b) Use substitution u = ln x with du/dx = 1/x.
1
dx =
x ln x
1
du = ln u
Tufts University
Department of Mathematics
Math 11, Final Exam
Thursday, December 11, 2008
8:3010:30 a.m.
No books, notes or electronic devices of any kind are allowed. Please do all of your work in the blue book. Remember
to sign your exam book. With you
Tufts University
Department of Mathematics
Exam 2 Review Problems
Math 11
Fall, 2008
dy
dx .
Do not simplify.
(a) y = cos1 ( 1 + x2 x)
(d) exy = arcsin x
(b) y = ln x + 2e + 5x + x7 + log3 x + ln 8 + e4x
(e) y = (5x + 2)cos x
(c) y = tan1 (sin x2 cos x2 )
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Tufts University
Department of Mathematics
Exam 1
Math 11
February 28, 2011
You may not use books, notes, or calculators during the exam. Solutions must be written in your exam
book; cross out any work you do not want graded. You are required to sign your
Tufts University
Department of Mathematics
Final Exam
Math 11
May 9, 2011
8:30 10:30 AM
You may not use books, notes, or calculators during the exam. Solutions must be written in your exam
book; in all problems, you must show all your work in order to rec
Tufts University
Department of Mathematics
Exam 2
Math 11
April 11, 2011
You may not use books, notes, or calculators during the exam. Solutions must be written in your exam
book; cross out any work you do not want graded. You are required to sign your ex
Math 11: Calculus I
Tufts University
Department of Mathematics
Review Problems for Exam 2
Summer Session I 2010
1. Evaluate.
19
.
(a) sin
sin
6
(b) cos tan1
.
3
1
(c) sin1
2
2
cos1
.
2
2
(d) sin(cos1 x).
dy
2. Find dx . Do not simplify. Note that some pr
Math 11: Summer session II
Solutions to Review Problems for Exam 1
July 15, 2010
Note: odd problems from the book have solutions in the back of the book.
1. Calculating derivatives : Page 262 problems 123 odd (skip 15 and 21).
2. Page 168, number 47.
3.
Tufts University
Math 11
Department of Mathematics
February 19, 2009
Exam 1
You may not use books, notes, or calculators during the exam. Solutions must be written in your exam
book; cross out any work you do not want graded. You are required to sign your
Tufts University
Department of Mathematics
Exam 1 Solutions
Math 11
Spring 2009
1
1. (a) log9 31 = log9 91/2 =
2
3
2
=
(b) sin
3
2
(c) log15 (1/2) + log15 (30) = log15 (1/2 30) = log15 (15) = 1
3
3
2. (a) . In the rst quadrant of the unit circle, cos =
Tufts University
Department of Mathematics
Exam II
Math 11
November 10, 2008
No books, notes, or calculators are allowed on the exam. Please do all of your work in the blue book.
Remember to sign your exam book. With your signature, you are pledging that
Tufts University
Department of Mathematics
Final
Math 11
May 4, 2007
8:3010:30
No books, notes, or calculators are allowed on the exam. Please do all of your work in the blue book.
Remember to sign your exam book. With your signature, you are pledging th