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/Geo (M. Kohandel)
Civil/Enviro/Geo (R. Begg)
Mechanical
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
of variable (equivalently, by substitution).
Students w
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 computing the volume of solid by
cylindrical shells means
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 computing the volume of solid by
cross-section means,
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 F(x) on
the mass m over the distance d is.
Students wh
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 to hydrostatic pressure.
Students who have practiced t
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 and with respect to the y-axis is, about the center of
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.)
Students who have mastered the content of this lecture kn
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, continuity from the left or right of a, a function bein
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, average rate of change of a function over an interval, the t
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 trig functions, the derivative of arcsin x, arcos x, arct
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 function f(x).
Students who have practiced the techniques p
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 general antiderivative of a function, the indefinite int
University of Waterloo
MATH 116 Fall 2008
Final Exam
Friday, December 12, 2008 (4:00-6:30 pm)
Name (print): _
ID Number: _
Signature: _
Please indicate your section:
Chemical (R. Malinowski)
Mechanical (R. Malinowski)
Mechanical (G. Stubley)
Management (Z
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 derivative test, concavity,
what defines concave upwards and c
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, area, net area
Students who have practiced the techniqu
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 to absolute max and min of a function.
Students who have
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 defines concave upwards and concave downward, inflection p
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 who have practiced the techniques presented in this lectu
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 practiced the techniques presented in this lecture will be
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
the definite integral.
Students who have practiced the t
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 calculus, the
definition of antiderivative and the genera
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
over an interval [a, b], the mean value theorem for integr
Friday, September 30 Lecture 10 : Differentiation of trig functions and
exponential functions. (Refers to section 3.3 in your text)
Students who have mastered the content of this lecture know about:
The derivatives of trig functions, the derivatives of ex
Tuesday, October 4 Lecture 12 : Implicit differentiation, logarithmic differentiation,
higher-order derivatives (Refers to section 3.8 and 4.3 pp. 260-64)
Students who have mastered the content of this lecture know about: The derivatives of log functions,
Thursday, October 6 Lecture 13 : Differentials and linearization. (Refers to Section 4.1 in
your text)
Students who have mastered the content of this lecture know about: The definition of the differential of a function
f(x), the linearization of f(x) near
Friday, November 6 Lecture 23: Indeterminate forms and lHpitals rule (Refers
to Section 4.11 in your text (D. Trim)
Students who have mastered the content of this lecture know about: LHpitals rule.
Students who have practiced the techniques presented in t
Monday, November 16 Lecture 28 : Fundamental theorem of calculus. (Refers to
Section 6.3 and 6.4 in your text)
Students who have mastered the content of this lecture know: The Fundamental theorem of calculus, the
definition of antiderivative and the gener
Wednesday, November 11 Lecture 25: Riemann sums (Refers to Section 6.1 and
6.2 in your text (D. Trim)
Students who have mastered the content of this lecture know about: Sigma notation, Riemann sums
Students who have practiced the techniques presented in t
Wednesday, November 18 Lecture 29 : Antiderivatives (Refers to Section 6.xx in
your text)
Students who have mastered the content of this lecture know about: The Fundamental theorem of
calculus, the general antiderivative of a function, the indefinite inte
Math 116
[1]
Lab #9 Solutions
Fall 2013
1. Use the Second Fundamental Theorem of Calculus to find the derivative of:
Z x
(a) Given f (x) =
(2 + t4 )5 dt
0
0
Solution: Applying the fundamental theorem: f (x) = (2 + x4 )5
[2]
(b) Given f (x) =
Z
2
cos(t2 )
Math 116 - Lab #9 - Fall 2013.
Topics: Fundamental Theorem of Calculus (Parts I and II), Definite/Indefinite
integrals, Integration by substitution, Integration by parts.
(Sections 6.4, 6.5, 6.7, 8.1, and 8.2 of Trim).
You are to provide full solutions to
Math 116 - Lab #1 - Fall 2013.
Topics: Polynomials, Equations of Lines, Conic Sections, Symmetry, Inverse
Functions. (Sections 1.2 to 1.6 of Trim).
You are to provide full solutions to the following problems. You are permitted to discuss the
problems with
Math 116 - Lab #10 - Fall 2013
Topics: Average Value, Area Between Curves and Volumes of Solids of Revolution.
(Sections 6.6, 7.1 and 7.2 of Trim).
You are to provide full solutions to the following problems. You are permitted to discuss the
problems with