Amherst College
Department of Mathematics
Math 111.03
Practice Exam 1
Fall 2015
Name:
Read This First!
Please read each question carefully. Show ALL work clearly in the space provided.
In order to receive full credit on a problem, solution methods must
Amherst College, DEPARTMENT OF MATHEMATICS
Math 11, Final Examination, May 14, 2010
This is a closed-book examination. No books, notes, calculators, cell phones, communication
devices of any sort, or other aids are permitted.
You
need3 not simplify alg
Math 111, Introduction to the Calculus, Fall 2011
Midterm II Practice Exam 1 Solutions
1. Find the derivative of each of the following functions (no explanation is necessary, but
it may help you get the correct answer if you show your work):
(a) f (x) = 2
Math 111, Fall 2011: Midterm I Study Guide
The first midterm will take place on Friday 30 September at 9:00am in Seeley Mudd 206. It
will be 50 minutes long. You will not be allowed to use notes, books or calculators of any kind.
The exam will cover secti
Math 111, Introduction to the Calculus, Fall 2011
Final Exam Solutions
1. (5 points each) Calculate each of the following limits. You should say if the limit is
equal to a particular value, is or if it does not exist.
|x|
x0 x2
Solution: For x > 0, |x|/x2
Math 111, Introduction to the Calculus, Fall 2011
Midterm III Practice Exam 1 Solutions
1. Find the critical points of the function
f (x) = x2 (x + 1)2
For each critical point, decide if it is a local maximum or local minimum, or neither.
The critical poi
Math 111, Fall 2011: Midterm III Study Guide
The third midterm will take place on Friday 2 December at 9:00am in Seeley Mudd 206. It will
be 50 minutes long. You will not be allowed to use notes, books or calculators of any kind. The
exam will cover secti
Math 111, Introduction to the Calculus, Fall 2011
Midterm I Solutions
1. Sketch, on separate diagrams, graphs of the following functions for the range 0 x 2:
(a) cos(x)
(b) cos(2x)
(c) cos x
2
(d) cos 2x
2
For parts (b), (c) and (d) explain how you obt
Math 111, Introduction to the Calculus, Fall 2011
Midterm II Practice Exam 2 Solutions
1. (a) State the product rule for finding the derivative of a product f (x)g(x) of two
functions f and g.
(b) Use the product rule to show that the derivative of
3
f (x
Answer Key, Math 11, Final Examination, December 19, 2009
1. [20 Points] Evaluate each of the following limits. Please justify your answers. Be clear if the
limit equals a value, + or , or Does Not Exist.
(a) lim
4
x2 + x 6
= by Direct Substitution
2
x 6x
Math 111, Introduction to the Calculus, Fall 2011
Midterm III Practice Exam 1
You will have 50 minutes for the exam and are not allowed to use books, notes or calculators.
Each question is worth 10 points.
1. Sketch a graph of the function
x2 1
x2 + 1
to
Amherst College
Department of Mathematics
Math 111.03
Practice Exam 1
Fall 2015
Name:
Read This First!
Please read each question carefully. Show ALL work clearly in the space provided.
In order to receive full credit on a problem, solution methods must
Amherst College
Department of Mathematics
Math 111.03
Practice Exam 2
Fall 2015
Name:
Read This First!
Please read each question carefully. Show ALL work clearly in the space provided.
In order to receive full credit on a problem, solution methods must
Amherst College
Department of Mathematics
Math 111.03
Exam 1
Fall 2015
Name:
Read This First!
Please read each question carefully. Show ALL work clearly in the space provided.
In order to receive full credit on a problem, solution methods must be comple
Amherst College, DEPARTMENT OF MATHEMATICS
Math 11, Final Examination, May 14, 2010
Answer Key
1. [20 Points] Evaluate each of the following limits. Please justify your answers. Be clear if the
limit equals a value, + or , or Does Not Exist.
3
14
3
x2 4x
Amherst College, DEPARTMENT OF MATHEMATICS
Math 11 Final Examination, December 22, 2010
Answer Key
This examination booklet consists of 12 problems on 15 numbered pages. If you have received a
defective copy, please notify your instructor immediately.
T
Math 11
Final Examination
May 11, 2011
Answer Key
1. [20 Points] Evaluate each of the following limits. Please justify your answers. Be clear if the
limit equals a value, + or , or Does Not Exist.
0
x2 1
= lim
= 0 by DSP
2
(x + 1) 1 x1 4 1
(a) lim
x1
(b)
Math 111, Introduction to the Calculus, Fall 2011
Midterm I Practice Exam 2 Solutions
1. Prove, using the precise definition of limit, that the function
f (x) = x
is continuous at x = 1.
Solution: We want to show that
lim f (x) = f (1)
x1
that is
lim (x)
Math 111, Fall 2011: Midterm II Study Guide
The second midterm will take place on Friday 28 October at 9:00am in Seeley Mudd 206. It will
be 50 minutes long. You will not be allowed to use notes, books or calculators of any kind. The
exam will cover secti
Math 111, Introduction to the Calculus, Fall 2011
Midterm I Practice Exam 1 Solutions
For each question, there is a model solution (showing you the level of detail I expect on the
exam) and then below that are further comments.
1. (a) Use scaling and tran
Math 111, Introduction to the Calculus, Fall 2011
Midterm III Solutions
1. Calculate the following integrals
Z 4
1
dx
(a)
x
1
Z 0
(b)
sin(2t) dt
/2
(a) Since
1
x
= x1/2 we have
Z
4
x
1/2
1
x1/2
dx =
1/2
x=4
x=1
1/2
= 2(4 ) 2(11/2 )
=42
=2
(b) We can gues
Amherst College, Math 11 Final Examination, December 22, 2010
This is a closed-book examination. No books, notes, calculators, cell phones, communication
devices of any sort, or other aids are permitted.
You
need3 not simplify algebraically complicated
Math 111 Final, Manack, Fall 11.
You have 3 hours to take the nal. No calculators, notes, books, cell phones, communication
devices or aids of any sort are allowed. Show all your work and justify all your answers.
There are 14 problems on this nal, totall
Final Exam, Math 111-04, Fall 2012
Wednesday, December 19, 2012
Name:
Instructions: Do all the problems, and show all work, on your exam paper. If you
need more space, you may use additional sheets of paper and staple them to the
exam.
Little or no credit
Math 111, Section 01, Fall 2011
Final Exam
1. (20 points) Compute the following derivatives.
d x
a.
[e sin(5x)]
dx
x
csc(et ) dt.
b. F (x), where F (x) =
e
dy
, where e2x ey + xy = e2 .
c.
dx
d. G (ln(3), where G(x) = h(ex ) and it is known that h(3) = 2
Math 111 Final Exam
Dec. 19, 2012
1. (5 points each) Compute each of the following limits. You should say if the limit is
equal to a particular value, if it is , or if it does not exist.
x2 + 3x + 2
.
x2 x2 + x 2
x2 1
(b) lim
.
x1 (x 1)2
2x 2
.
(c) lim
x2
Math 111, Spring 2013
Final Exam, Math 111, Spring 2013
Instructions: Do all the problems, and show all work, including scratch work, on your exam
paper. If you need more space, use the back of any page.
Little or no credit may be awarded, even when your
Math 111, Introduction to Calculus, Fall 2012
Final Exam
Wednesday 19 December
You have 3 hours for this exam.
You may not use books, notes, calculators, cell phones or any other aids.
You must explain your answers clearly and completely to get full cr
Math 111
Final Exam
1. Evaluate each of the following limits.
[15]
x2 + 5x + 6
x! 3 x2 + 2x
3
4 2x
(b) lim
x! 1 5
x + 3x2
2
x
x 2
(c) lim 2
x!2 x
4x + 4
(a) lim
(d) lim
4
x
x! 4
1
x+3
x+4
2. Compute each of the following derivatives.
x
(a) f 0 (x), where
Math 111
Final Examination
December 19, 2012
This is a closed-book examination. No books, notes, calculators, cell phones, communication
devices of any sort, webpages, or other aids are permitted.
You need not simplify algebraically complicated answers.
Math 111, Introduction to the Calculus, Fall 2011
Midterm III Practice Exam 1
You will have 50 minutes for the exam and are not allowed to use books, notes or calculators.
Each question is worth 10 points.
1. Find the critical points of the function
f (x)
Math 111, Fall 2011: Final Exam Study Guide
The final exam will take place on Monday 19 December at 2:00pm in Seeley Mudd 206. It will
be 3 hours long. You will not be allowed to use notes, books or calculators of any kind. The
exam will cover material fr
Math 11
Final Examination
May 11, 2011
This is a closed-book examination. No books, notes, calculators, cell phones, communication
devices of any sort, or other aids are permitted.
You
need3 not simplify algebraically complicated answers. However, nume
Math 111, Introduction to the Calculus, Fall 2011
Midterm III Practice Exam 1
You will have 50 minutes for the exam and are not allowed to use books, notes or calculators.
Each question is worth 10 points.
1. Sketch a graph of the function
x2 1
x2 + 1
to
Math 111, Introduction to the Calculus, Fall 2011
Midterm II Practice Exam 1
This exam is intended to give you an idea of the length and difficulty of the real thing.
Please remember that topics not on covered here could definitely still appear on the exa