University of Waterloo
Final Examination
Fall Term 2012
Name (Please Print Legibly)
Signature
Student ID Number
COURSE NUMBER
Math 116
COURSE TITLE
Calculus 1 for Engineering
COURSE SECTIONS
001 002 0
Thursday, November 10 Lecture 25 : Fundamental theorem of calculus. (Refers to
Section 5.4, 5.5 in your text)
Students who have mastered the content of this lecture know: The Fundamental theorem of ca
Thursday, November 17 Lecture 28 : Average value of a function. (Refers to
Section 7.7 your text)
Students who have mastered the content of this lecture know: About the average value of a function
ove
Friday, November 11 Lecture 26 : Antiderivatives (Refers to Section 5.4, 5.5 in your
text)
Students who have mastered the content of this lecture know about: The Fundamental theorem of
calculus, the g
Friday, November 18 Lecture 29 : Curve length. (Refers to Section 7.1 your text)
Students who have mastered the content of this lecture know: About the curve length or arclength of the
curve of a func
Tuesday, November 15 Lecture 27 : Integration by substitution (Refers to Section
6.1 your text)
Students who have mastered the content of this lecture know: About differentials, integration by change
Thursday, November 24 Lecture 31 : Volumes of solids of revolution: cylindrical
shells method. (Refers to Section 7.3 in your text)
Students who have mastered the content of this lecture know: what co
Tuesday, November 22 Lecture 30 : Volumes of a solid of revolution: Crosssection (slicing) method (Refers to Section 7.2 in your text)
Students who have mastered the content of this lecture know: what
Friday, November 25 Lecture 32 : Applications : Work and energy (Refers to Section 7.4 in
your text)
Students who have mastered the content of this lecture know: what the amount of work W performed by
Thursday, December 1 Lecture 34 : Hydrostatics (Refers to Section 7.6 in your text.)
Students who have mastered the content of this lecture know: the basic principles of the force
exerts on a wall due
Tuesday, November 29 Lecture 33 : The center of mass (Refers to Section 7.5 in your
text)
Students who have mastered the content of this lecture know: what the first moment wither respect to the xaxis
Tuesday, September 20 Lecture 5 : Continuation of lecture on Limits (Refers to
Section 2.1 to 2.3 in your text) (Note: This is the continuation of lecture 4 and so its content appears as the same.)
St
Tuesday, November 8 Lecture 24 : Properties of definite integrals (Refers to
Section 5.2 in your text)
Students who have mastered the content of this lecture know about: The elementary properties of
t
Thursday, November 3 Lecture 22: Riemann sums (Refers to Section 5.1 in your
text)
Students who have mastered the content of this lecture know about: Sigma notation, Riemann sums
Students who have pra
Tuesday, November 1 Lecture 21: Indeterminate forms and lHpitals rule
(Refers to Section 4.5 in your text)
Students who have mastered the content of this lecture know about: LHpitals rule.
Students wh
University of Waterloo
Department of Applied Mathematics
MATH 116 Calculus 1 for Engineering
Midterm Examination Fall 2005
October 25, 2005, 7 - 9 p.m.
NO CALCULA
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I.D.
University of Waterloo
Math 116 Calculus I for Engineering
Midterm Examination
Fall 2012
Time: 5:30 - 7:30 pm
Tuesday, October 16th.
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Signature:
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University of Waterloo
Math 117 ~- Calculus I for Engineering
Midterm Examination Fall 2011
Monday, October 17th. H I, Time: 9:00 - 10:30am
Name (print):
LD. Number:
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University of Waterloo
MATH 116 - Fall 2007
Midterm Exam
Tuesday, October 23, 2007 (7:00-9:00 pm)
Name (print): _
mNumbenf
Signature:
ECIJD
Please indicate your section:
® Chemical (R. Malinowski)
[
University of Waterloo
MATH 116 Fall 2009
Final Exam
Monday, December 14, 2009 (12:30-3:00 pm)
Name (print): _
ID Number: _
Signature: _
Please indicate your section:
Chemical (D. Park)
Civil/Enviro/G
University of Waterloo
MATH 116 Fall 2008
Final Exam
Friday, December 12, 2008 (4:00-6:30 pm)
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Chemical (R. Malinowski)
Mechanica
Tuesday, October 25 Lecture 18 : Derivatives and the shape of a graph. (Refers to
Section 4.3 and 4.4 in your text)
Students who have mastered the content of this lecture know about: The First derivat
Friday, November 4 Lecture 23 : The definite integral (Refers to Section 5.2 in your
text)
Students who have mastered the content of this lecture know about: The definition of the definite
integrals,
Friday, October 28 Lecture 20 : Optimization problems (Refers to Section 4.7 in
your text)
Students who have mastered the content of this lecture know about: Optimization problem and how they
relate t
Thursday, October 27 Lecture 19 : Curve sketching (Refers to Section 4.6 in your
text)
Students who have mastered the content of this lecture know about: The First derivative test, concavity,
what def
Thursday September 22 Lecture 6 : Continuous functions. (Refers to Section 2.5 in
your text)
Students who have mastered the content of this lecture know about:
The definition of f is continuous at a,
Thursday September 22 Lecture 7 : Differentiation. (Refers to Section 3.1 and 3.2
of your text)
Students who have mastered the content of this lecture know about:
The definition of tangent line, avera
Friday, September 30 Lecture 11 : Derivatives of the inverse of functions. (Refers
to Section 3.7 in your text)
Students who have mastered the content of this lecture know about:
The inverse of the tr
Friday, November 13 Lecture 26 : The definite integral (Refers to Section 6.3 in
your text (D. Trim)
Students who have mastered the content of this lecture know: The definition of the definite integra
MATH 116 Midterm Review Questions
1. Let f (x) =
5x 1 and g(x) = x2 .
(a) Find f 1 (x)
(b) Find the domain and range of f (x).
(c) What is the domain of g f (x)?
2. (a) Write
2
3x if x < 1
f (x) = ex
Instructions
1. Write your student ID number and UW userid at the top of this page.
2. Answer the questions in the spaces provided. There are questions on
both sides of the page. There is a blank page
MATH 116 Fall 2017
Practice Solutions 2
1. For the given functions, decide whether the function is even, odd, or neither.
(a) f (x) = 5x6 2x4 + x2 + 1 (b) g(x) = 3x5 + x3 x + 1
Solution:
(a) f (x) = 5
13
13.1
Week 13
Arc Length
In this section we will need to recall a couple of things from earlier sections:
Mean Value Theorem: If f is continuous on [a, b], dierentiable on (a, b), there exists c 2