Review for exam over Ch. 2 & 3 in MATH F151X
If f ( x ) = x 2 3x , g ( x ) = 2x + 5 , m ( x ) = x 4 , and p ( x ) =
1a.
Find (g m)(8) and state its domain.
b.
Find (g f )(5) and state its domain.
c.
d.
2x + 5
3x 1
Find x so that p ( x ) = 10 .
Find ( f g
Mar 23, 2016
Math 122X Exam 2
The exam is closed book, closed notes and you may not use a calculator. Show your
work to get full credit.
1. (12 pts) For the quadratic function f (x) = 2x2 + 8x + 6, answer the following:
(a) (3pts) Find the vertex of the p
Feb 15, 2016
Math 122X Exam 1
The exam is closed book, closed notes and you may not use a calculator. Show your
work to get full credit.
1. (4pts) Let A = cfw_2, 4, 6, 8, 10, 12, 14, 16, 18, B = cfw_3, 6, 9, 12 and C = cfw_4, 9, 16, 25.
(a) Find A B C.
(b
Dec 2, 2016
MATH 122X Exam 3
1. (5 pts) Are the following equations linear equations?
7x + 5y 7yz = 0
5xy + x 7 = 0
x + 2y + 7z = 97
10w +
2u 3v 7 = 0
2. A matrix is given below in row-echelon form.
1 2 3 1
0 1 3 0
0 0 2 2
(a) (4 pts) Write the system o
DEVM F105N
Review: Ch. 6, 8, and 9
Show all work in each problem. Round decimal answers to four places.
1.
Combine into a single log term: log 2 ( x 1) + 3log 2 ( 2 ) 2log 2 ( 2x + 5 )
( 3 ) log ( )
1
2 8
2a.
Evaluate. log3
b.
Evaluate. 53log5 2 + ln e 4
Political Economy Exam #1, Spring 2017
Study Guide Subject to a few changes
Part I Definitions: Write the letter of the definition in front of the correct term. The first one is done for you.
1 point
Term
Definition/Meaning
1) R
SWEET
2)
Specialization
3)
Math 113Final Review
Chapter 1 Voting Methods
1. (a) The result of the pairwise comparison between C and D is
15/12 C wins.
(b) The Borda count total for candidate B is 61.
4(6) + 3(5) + 2(6) + 1(10)
(c) The plurality winner is A.
Round
1
2
(d) The plural
Workshop
Key
Chapter 17 Review Questions
1. If the middle 95% of a normal distribution lies between 120 and 160, what is the mean and standard deviation of the distribution?
(120 160) / 2 140
Since 131 is 2 standard deviations to the right of the mean, (
Math 113: Workshop 3
Key
1. A French restaurant offers a menu consisting of 2 soups, 4 salads, 9 main courses, and 5 desserts. A fixed-price lunch consists of a choice of
soup or salad or both, a main course and a dessert. How many are there?
(2 + 4 + 2x4
Math 103: Workshop 2
Chapters 5-7: Graph Theory
1. (a) List 2 properties that apply to all graphs.
1. The sum of the degrees of all the vertices is equal to twice the number of edges.
2. There are always an even number of odd degreed vertices.
(b) List 3
Math 103: Workshop 2, part A
Name: _
Chapters 5-7: Graph Theory
1. (a) List 2 properties that apply to all graphs.
(b) List 3 properties of trees.
2. Explain the difference between an Euler circuit and a Hamilton circuit.
3. Consider a K 20 .
4. How many
Math 103: Workshop 1
Name: _
Chapter 1 Review Questions
1. Consider the given preference schedule.
# of Voters
10
6
5
4
2
1st choice
A
B
C
D
D
(a) The Borda count total for candidate C is _.
2nd choice
C
D
B
C
A
3rd choice
D
C
D
B
B
4th choice
B
A
A
A
C
(
Math 103: Workshop 1A
Chapter 1 Review Questions
1. Consider the given preference schedule.
N = 27
(a) The Borda count total for candidate C is 76.
4(5) + 3(14) + 2(6) + 1(2) = 76
(b) The winner of the pairwise comparison between C and D is C. The point s
MATH 302 Differential Equations (Bueler)
16 April 2009
Selected Solutions to Assignment #8
These problems were graded at 3 points each for a total of 24 points.
5.2 #2.
Rewrite as
(i)
Dx 3y = 0
(ii)
2x + (D + 1)y = 0.
Combine by 2(i) + D(ii) to get: D(D +
MATH 302 Differential Equations (Bueler)
REVISED 24 March 2009
Selected Solutions to Assignment #5
(Revised 4.3 #4.)
These problems were graded at 3 points each for a total of 27 points.
4.1 #2.
(b)
(a)
m(cy)00 + b(cy)0 + k(cy) = c(my 00 + by 0 + ky) = c(
MATH 302 Differential Equations (Bueler)
16 February 2009
Selected Solutions to Assignment #3
These problems were graded at 3 points each for a total of 27 points.
2.4 #6.
2.4 #10.
separable, linear (and not exact)
It is exact because
1=
N
M
=
= 1.
y
x
Be
MATH 302 Differential Equations (Bueler)
28 February 2009
Solutions to Assignment #4
These problems were graded at 3 points each for a total of 21 points.
3.4 #2. This problem fits into the framework of Example 1. In particular, we are told b = 10 and g =
MATH 302 Differential Equations (Bueler)
24 March 2009
Selected Solutions to Assignment #6
These problems were graded at 3 points each for a total of 21 points.
(The Group Project on A#6 is treated as a separate 10 point assignment.)
4.4 #10.
The auxiliar
MATH 302 Differential Equations (Bueler)
2 April 2009
Selected Solutions to Assignment #7
These problems were graded at 3 points each, except for 4.9 #4 which was 6 points, for a total of 21 points.
4.7 #33. The answer Ctet is in the back of the book. To
MATH 302 Differential Equations (Bueler)
1 May 2009
A Solution, from Assignment #11
Recall Assignment #11 is NOT DUE!
8.2 #8.
(d) We have the series
cos x = 1
X
x2 x4
x2j
+
=
(1)j
2!
2!
(2j)!
j=0
2j
x
It is easiest to apply the original ratio test with
MATH 302 Differential Equations (Bueler)
1 May 2009
Selected Solutions to Assignment #10
These problems were graded at 5 points each for a total of 25 points.
7.5 #4.
The Laplace transform of the ODE, including the initial values, is
2
1
s Y (s) sy(0) y
MATH 302 Differential Equations (Bueler)
18 February 2009
Selected Solutions to Assignment #2
Revised. Corrections in 2.2 #12 and 2.3 #8.
1.4 #8.
The full table of my Eulers method calculations looks like this:
steps
x
0
1
2
4
8
y
y
y
y
0
0
0
0
8
4
3
8
2
MATH 302 Differential Equations (Bueler)
2 February 2009
Selected Solutions to Assignment #1
These problems were graded at 3 points each for a total of 27 points.
1.1 #4.
PDE, second order, dependent variable is u, independent are x and y
1.1 #14.
dx
= kx
MATH 302 Differential Equations (Bueler)
27 April 2009
Selected Solutions to Assignment #9
These problems were graded at 3 points each for a total of 27 points.
7.2 #4.
An integration-by-parts:
Z
Z
t= Z
(3 s)1 e(3s)t dt
L te3t (s) =
est te3t dt =
te(3s
Math F401: Introduction to Real Analysis
Fall 2016 Syllabus
Course Description
This course is a rigorous study of the ideas underlying calculus and an introduction to the
real numbers. Rather than the computational focus of your previous calculus classes,
Math 401: Homework 2
Due September 12, 2016
Solutions
Exercise 1.4.1: Recall that I stands for the set of irrational numbers.
(a) Show that if a, b Q then ab and a + b Q as well.
(b) Show that if a Q and t I then a + t I and if a , 0 then at I as well.
(c
Math F401: Homework 5 Solutions
October 6, 2016
1. Suppose cfw_n j
j=1 is a sequence of natural numbers such that n j < n j+1 for all j N. Show
that n j j for all j N
2. Show that a subsequence of a convergent sequence converges to the same limit. Be sur