Wednesday, January 11 Lecture 6 : Rational functions : Partial fractions (Refers
to Section 6.5 of your text)
After having practiced the problems associated to the concepts of this lecture the student
should be able to: Solve integrals containing rational
Exam ID#000353-00
Course: MATH 118 Term: W2000 Type: M Solutions: S
Exam ID#000353-01
Course: MATH 118 Term: W2000 Type: M Solutions: S
Exam ID#000353-02
Course: MATH 118 Term: W2000 Type: M Solutions: S
Exam ID#000353-03
Course: MATH 118 Term: W2000 Type
Time: 2 hours
Instructors: [J Chem / Enviro Chem R. Malinowski
E] Civil R. Malinowski
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[3/ Mechanical M. Schpigel
No Additional Materials Allowed
Instructions:
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MATH 118, Calculus 2, Midterm, Feb 11th, 2004 Note: Questions not relevant to this years test have been omitted. 1: Evaluate each of the following integrals: a) b) c) d) e) cos3 d arctan x dx
x x2 +4x+13 x3 (x2 +2)2 1 4x2
dx dx
dx
x
2: Given that ex sin x
MATH 118, Calculus 2, Midterm, June 6th, 2005 Note: Questions not relevant to this years test have been omitted. 1: Integration. Solve the following integrals: a) c) tan2 x sec4 x dx 2x2 + 12x 10 dx b)
x+2 (x+3)(x2)
dx
d) e) f)
x2 sin x dx dx
1 x 1 (1x2 )
Mal'ln 7
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Faculty of Mathematics
University of Waterloo
Math 118
Midterm Winter 2007
Time: 2 hours
Last Name: 3
Date: Feb 5, 2007.
First Name:
ID. Number: Signature:
Instructors:
El/ Chemical Eng. R. Willard
E] Civil Eng. M. Best
E!
University of Waterloo, Waterloo, Ontario
Math 118
Midterm Examination
Time: 2 Hours Date: June 1i], sees
ND CALCULATORS or EITHER AIDS PERMITTED
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Wednesday, March 14 Lecture 29 : Binomial series (Refers to Section 8.8 in your
text)
After having practiced the problems associated to the concepts of this lecture the student should be able to:
State and apply the Binomial series theorem.
29.1 Introduct
Tuesday, March 13 Lecture 28 : Taylor's remainder theorem: Convergence of a
series to its generator (Refers to Section 8.8 in your text)
After having practiced the problems associated to the concepts of this lecture the student should be able to:
Define t
Monday, January 16 Lecture 7 : Improper integrals. (Refers to section 6.6 in your
text.)
After having practiced the problems associated to the concepts of this lecture the student
should be able to: Recognize the two different types of improper integrals,
Wednesday, January 18 Lecture 9 : Error estimation for numerical integration.
(Refers to section 5.3)
After having practiced the problems associated to the concepts of this lecture the student should
be able to: Find error's bounds when applying either th
Wednesday, January 25 Lecture 12 : Second-order Differential equations. (Not
explicitly discussed in your text)
After having practiced the problems associated to the concepts of this lecture the student should
be able to: Solve second-order differential e
Thursday, February 10 Lecture 20 : Alternating series (Refers to Section 8.2 in
your text)
After having practiced the problems associated to the concepts of this lecture the student should
be able to: Define an alternating series, state the alternating se
Monday, February 27 Lecture 21 : Absolute convergence and conditional
convergence. (Refers to Section 8.5 in your text)
After having practiced the problems associated to the concepts of this lecture the student
should be able to: Define "converges absolut
Tuesday February 28 Lecture 22 : Ratio test and Root test. (Refers to Section 8.5 in
your text)
After having practiced the problems associated to the concepts of this lecture the student should be
able to: Apply the ratio test and the root test to determi
Wednesday, February 29 Lecture 23 : Error bounds for series approximations.
(Refers to Section 8.2 and 8.3 in your text)
After having practiced the problems associated to the concepts of this lecture the student should be
able to: Approximate the value of
Monday, March 5 Lecture 24 : Power Series and their interval of convergence.
(Refers to Section 8.6 in your text)
After having practiced the problems associated to the concepts of this lecture the student
should be able to: Define a power series centered
Tuesday, March 6 Lecture 25 : Expressing a power series as a function and
operations on power series. (Refers to Section 8.7 )
After having practiced the problems associated to the concepts of this lecture the student should be
able to: Determine the sum,
Wednesday, March 7 Lecture 26 : Expressing functions as a power series:
Derivatives and Integrals of power series. (Refers to Sections 8.6 and 8.7 )
After having practiced the problems associated to the concepts of this lecture the student should be
able
Monday, March 12 Lecture 27 : Taylor series and Maclaurin series generated by a
function f(x). (Refers to Section 8.8 your text)
After having practiced the problems associated to the concepts of this lecture the student should be able to:
Define a Taylor
Math 118 Spring 2016: Practice Problems 1
1. Compute the following:
Z
Z 2
2
(2x 3x + 1) dx (b)
(a)
1
1
+7
1 + x2
dx
d
(c)
dx
Z
2x
cos(et ) tan(ln(t) dt
cos(x)
2. Use the method of substitution to find the following:
Z
Z
Z
2
3
2
(cos (x) sin(x) + 3 sin(x