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Midterm

MATH141 Winter 2011 ExamExam


Department
Mathematics and Statistics
Course Code
MATH 141
Professor
All
Study Guide
Midterm

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VERSION 1
McGill University — Faculty of Science
FINAL EXAMINATION
MATHEMATICS 141 2011 01 CALCULUS 2
EXAMINER: Professor S. W. Drury DATE: Friday April 15, 2011
ASSOCIATE EXAMINER: Professor N. Sancho TIME: 9 am. to noon
FAMILY NAME:
GIVEN NAMES:
MR, MISS, MS, MRS, &c.: STUDENT NUMBER:
If you expect to graduate in Spring 2011 put an ×in this box:
Instructions
1. Fill in the above clearly. Enter your name as it appears on your student card.
2. Do not tear pages from this book; all your writing — even rough work — must be handed in. You
may do rough work anywhere in the booklet except in the box below and in the answer boxes.
3. This is a closed book examination. Calculators are not permitted, but regular and translation
dictionaries are permitted.
4. This examination consists of two parts, Part A and Part B. READ CAREFULLY THE MORE
DETAILLED INSTRUCTIONS AT THE START OF EACH PART.
5. Part A has 20 multiple choice questions each of which is worth 2 points for a total of 40 points.
It is recommended that in the first instance, you do not spend more than 4 minutes per question
or 75 minutes in total on Part A.
6. Part B has five questions worth a total of 46 points which should be answered on this question
paper. The questions in part B are of two types:
In BRIEF SOLUTIONS questions, each answer will be marked right or wrong. Within a
question, each answer has equal weight.
In SHOW ALL YOUR WORK questions a correct answer alone will not be sufficient unless
substantiated by your work. Partial marks may be awarded for a partly correct answer.
In Part B, you are expected to simplify all answers wherever possible.
7. This examination booklet consists of this cover, Pages 1–4 containing questions in Part A, Pages
5–10 containing questions in Part B and Pages 11–14 which are blank continuation pages.
8. A TOTAL OF 86 POINTS ARE AVAILABLE ON THIS EXAMINATION.
PLEASE DO NOT WRITE INSIDE THIS BOX
code 21 22 BS total
/8 /8 /16
23 24 25 SA total
/10 /10 /10 /30

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Calculus 2 MATH 141 Final Exam Version 1
Part A: MULTIPLE CHOICE QUESTIONS
Each of the following 20 questions is worth 2 points. Half of a point will be subtracted for
each wrong answer. The maximum number of points you may earn on these multiple choice
questions is 40 points. There is only one correct answer expected for each question. The
questions are to be answered on the answer card provided. Be sure to enter on the answer
card:
Your student number. Your name.
The check code, i.e. the first two letters of your family name.
Fill in the disks below your student number, check code and verify that the
marked version number matches the version number on the question paper. If
it does not, please notify an invigilator.
It is recommended that in the first instance, you do not spend more than 4 minutes per
question or 75 minutes in total on Part A.
Please note:
The Examination Security Monitor Program detects pairs of students with un-
usually similar answer patterns on multiple-choice exams. Data generated by
this program can be used as admissible evidence, either to initiate or corrob-
orate an investigation or a charge of cheating under Section 16 of the Code of
Student Conduct and Disciplinary Procedures.
1. (2 points) Evaluate the Riemann sum for Z4
2
x2dx which uses three intervals of equal
length and evaluation points at the midpoints of these intervals.
(a) 16, (b) 22, (c) 11, (d) 56
3, (e) 40.
2. (2 points) Find lim
n→∞
1
n
n
X
k=1
ln µ2n
n+k.
(a) ln(2) 1
2, (b) 1, (c) 1ln(2)
2, (d) 1 ln(2), (e) 2 ln(2) 1.
3. (2 points) Let F(x) = Zx
0p1 + t4dt. Then F(1) equals
(a) 2, (b) 1, (c) 2, (d) 1
2, (e) 1
2.
1

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Calculus 2 MATH 141 Final Exam Version 1
4. (2 points) Let the function be defined by
f(x) =
sin(x) if x < 0,
1cos(x) if x0.
Then for x0, Zx
π
f(t)dt =
(a) 2 + xsin(x), (b) xsin(x), (c) 2 + x+ sin(x), (d) x+ sin(x),
(e) x+ cos(x) + sin(x).
5. (2 points) Let f(x) = 2x
1 + x2. The Integral Mean Value Theorem applied to Z3
1
f(t)dt
asserts the existence of a number awith 1 a3 satisfying
(a) f(a) = 1
4, (b) f(a) = ln(5)
2, (c) f(a) = ln(5), (d) f(a) = 6
25,
(e) f(a) = 4
5.
6. (2 points) Zπ
π
2
sin(x) + cos(x)
sin(x)cos(x)dx =
(a) ln(2), (b) 1, (c) 0, (d) ln(2), (e) not defined.
7. (2 points) Zπ
π
2
sin(x)cos(x)
sin(x) + cos(x)dx =
(a) 1, (b) ln(2), (c) 0, (d) ln(2), (e) not defined.
8. (2 points) The area of the region bounded by the parabola x=y(y3) and the line
y=xis
(a) 37
6, (b) 9, (c) 32
3, (d) 8, (e) 5.
9. (2 points) Z1
1
arctan(x)dx =
(a) πln(4)
2, (b) πln(4)
4, (c) π, (d) 0, (e) πln(2)
4.
10. (2 points) The volume obtained by rotating the region x > 0, 0 y < x1exabout
the y-axis is
(a) π
2, (b) π, (c) 2π, (d) 4π, (e) infinite.
2
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