Math 231 - Practice Exam Due
This is a practice exam for Math 231. I suggest that you take it as a regular exam: set aside 50 minutes and put it aside at the end of that time. An solution set will be posted next week on the class website. Please che
Worksheet #1
Math 231
1
Knowledge Survey
This is a knowledge survey, not a test. Do not attempt to solve any of the problems. Instead, rate on the
provided 3-point scale your confidence in your ability to answer each question.
R
A. Evaluate esin() cos()d
Worksheet #13
Math 231
1
Knowledge Survey
This is a knowledge survey, not a test. Do not attempt to solve any of the problems. Instead, rate on the
provided 3-point scale your confidence in your ability to answer each question.
A. Could you use the (Direc
Worksheet #5
Math 231
Instructions: Put the first and last name of everyone in your group slip of paper supplied by your TA.
Everyone is to do their own worksheet but everyone in the group shares the same grade. Be sure to show
your work and explain your
Eriq Lucero
J.W. Morrissette
Theatre 101
31 March 2017
Technician/Director Assignment: Charity
A. Scenic Design
I would like to make the play somewhat realistic and present-day, since the play has
already been given a background: Bellagio. The setup aroun
Math 231E, Lecture 22.
Work, Average Value, Arclength, Surface Area
1
Work
We know from physics that work is force times distance. If we apply a constant force F over a distance
d, then the total amount of work done is W = F d. But what if the force depen
Math 231E, Lecture 20.
Improper Integrals
1
Examples of weirdness
Example 1.1. Let us consider the indefinite integral
Z
dx
.
(x 1)(x 2)
We will use partial fractions:
A
B
1
=
+
.
(x 1)(x 2)
x1 x2
We obtain
1 = A(x 2) + B(x 1).
If we plug in x = 1 this gi
Worksheet #12
Math 231
1
Knowledge Survey
This is a knowledge survey, not a test. Do not attempt to solve any of the problems. Instead, rate on the
provided 3-point scale your confidence in your ability to answer each question.
A. Explain why
P
n=1
1
n
di
Worksheet #16
Math 231
1
Knowledge Survey
This is a knowledge survey, not a test. Do not attempt to solve any of the problems. Instead, rate on the
provided 3-point scale your confidence in your ability to answer each question.
A. What does it mean for a
Worksheet #10
Math 231
Some questions on this worksheet reference a computer-generated demonstration (access it through Moodle)
to aid in conceptual understanding of the questions.
1
Knowledge Survey
This is a knowledge survey, not a test. Do not attempt
Worksheet #25
Math 231
1
Knowledge Survey
This is a knowledge survey, not a test. Do not attempt to solve any of the problems. Instead, rate on the
provided 3-point scale your confidence in your ability to answer each question.
A. Sketch the curve defined
Worksheet #6
Math 231
Instructions: Put the first and last name of everyone in your group slip of paper supplied by your TA.
Everyone is to do their own worksheet but everyone in the group shares the same grade. Be sure to show
your work and explain your
Worksheet #14
Math 231
1
Knowledge Survey
This is a knowledge survey, not a test. Do not attempt to solve any of the problems. Instead, rate on the
provided 3-point scale your confidence in your ability to answer each question.
A. What is the difference b
Worksheet #3
Math 231
Instructions: Put the first and last name of everyone in your group slip of paper supplied by your TA.
Everyone is to do their own worksheet but everyone in the group shares the same grade. Be sure to show
your work and explain your
Worksheet #7
Math 231
Some questions on this worksheet reference a computer-generated demonstration (access it through Moodle)
to aid in conceptual understanding of the questions.
1
Knowledge Survey
This is a knowledge survey, not a test. Do not attempt t
Worksheet #9
Math 231
1
Knowledge Survey
This is a knowledge survey, not a test. Do not attempt to solve any of the problems. Instead, rate on the
provided 3-point scale your confidence in your ability to answer each question.
A. Show that for any r 6= 1
Worksheet #15
Math 231
1
Knowledge Survey
This is a knowledge survey, not a test. Do not attempt to solve any of the problems. Instead, rate on the
provided 3-point scale your confidence in your ability to answer each question.
A. Does the series
P
(4)n (
Worksheet #28
Math 231
1
Knowledge Survey
This is a knowledge survey, not a test. Do not attempt to solve any of the problems. Instead, rate on the
provided 3-point scale your confidence in your ability to answer each question.
A. Evaluate
R
5 + 4x x2 dx
Math 231E, Lecture 23.
Sequences
1
Definitions and examples
Definition 1.1. A sequence is a (typically infinite) list of numbers.
The best description is having a formula for the nth term in the sequence:
an = n, or 1, 2, 3, 4, 5, . . . ,
1
1 1 1 1
an = ,
Math 231E, Lecture 21.
Volumes
1
Computing volumes
Recall the three steps behind every integration:
1. Break the object into n pieces
2. Approximate each piece (using smallness)
3. Add them back together!
For example, imagine that we have a volume whose c
Midterm 1 Mock Exam. Math 231 BD3. Spring 2015. 2/13/2015.
Trig identities: sin2 x + cos2 x = 1, tan2 x + 1 = sec2 x, sin 2x = 2 sin x cos x,
cos2 x = 21 (1 + cos 2x), sin2 x = 21 (1 cos 2x)
Multiple Choice Questions:
Z
1
1. What can we say about converg
Midterm 3 Mock Exam. Math 231 BD2. Spring 2015. 4/24/2015.
Multiple Choice Questions:
1. The sequence cfw_an = n1 :
(A) Converges
(B) Diverges
Determine whether each of these series diverges or converges:
2.
X
ecos(n) :
n=0
(A) Converges
3.
X
n ln(n)
n=2
Determine whether the following series converge or diverge:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
P
n4
n=1 3n5 2
P
3n2 1
n=3 7n4 +3
P
7n
n=1 1+12n
2 n
n=7 n6
P
P
n3
n=3 n8n
P
e1/n
n=1 n2
P
e1/n
n
P
8
n2 +9
n=1
n=1
P
n+4n
n=1 n+2n
P
5+3n
n=1 (4+n2 )3
P
a
Math 231/EL1 Exam I
Partial solution are at the end.
1. (8 points each) Evaluate the integral.
(a)
(b)
(c)
Z
cos3 (4x) dx
Z
x sec2 (9x) dx
Z
sec2 (x) sec(x) 1 tan(x) dx
q
2. (8 points each) Evaluate the integral.
(a)
Z
9 x2 dx
x2 + 3x + 1
dx
x2 + 3x 4
Z
d
Lucero 1
Eriq Lucero
J.W. Morrissette
Theatre 101
17 March 2017
Performance Review: Romeo and Juliet
1: Romeo and Juliets central conflict comes from the feud between the two main families: the
Capulets and the Montagues. It destroyed the opportunity for
Group: Name: soiuk on:
Math 231 A. Worksheet 15.
3.) Use the Maclaurin sgies for cosx to nd the Maclaurin series for f (m) m3 COS(.L 2.)
M * 3 .\ (1)
, (-03: ,. ( ='xc (1 = 1x323
cos) ,Eb (am. 5 F x) n :0 (2n)
'1! on n 9! +3
,8 24) (2'1 = Z (-11 (2.an
"
Math 231 U1 Spring 2017
Exam 2
March 17, 2017
Name:
Instructions:
Do not open the exam until instructed to do so.
This exam has 11 questions, for a total of 100 points. You have 50 minutes to complete this exam.
No electronic devices (smartwatches, cal