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 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
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
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
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, 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
Math 111, Introduction to the Calculus, Fall 2011
Midterm I Practice Exam 2
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 exam
Math 111, Introduction to the Calculus, Fall 2011
Midterm II Practice Exam 2
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
Math 111, Introduction to the Calculus, Fall 2011
Midterm I 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 exam
Math 130 Solutions Introduction to Statistics
Homework 2 Solutions
Assignment
Chapter 6: 8, 12, 19, 27, 29, 31, 36, 40, 41, 43, 45
Chapter 6
6.8] Checkup. The grandsons z-score is -1.88. This means that the boys height is 1.88
standard deviations below th
Math 130 Solutions Introduction to Statistics
Homework 1 Solutions
Assignment
Chapter 2: 18, 23
Chapter 3: 17, 19, 26, 45
Chapter 4: 8, 16, 40b, 45
Chapter 5: 9ab, 20, 26
Chapter 2
2.18] Flowers. Who 385 species of flowers. What Date of first flowering (i
Math 130
Homework 9 Solutions
Assignment
Chapter 9: 9.30, 9.32
Chapter 10: 10.16, 10.26, 10.32
Chapter 27: 27.2, 27.6, 27.14, 27.16, 27.28
Chapter 9
9.30] Unwed Births. Answers here can vary. You might decide the pattern is fairly linear, and
fit a linear
Math 130 Solutions Introduction to Statistics
Homework 4 Solutions
Assignment
Chapter 15: 2, 6, 20, 31, 43
Chapter 16: 9, 20, 24, 28, 47
Hint on 16.47] Think about the mean and standard deviation of a combination of six random variables, one for each
day