1
Math 009 Quiz 5
Topics from Week 6
Dr. Cheryl Cleaves
Fall OL4 2017
Name_
Instructions:
The quiz is worth 100 points. There are 10 problems, each worth 10 points. Your score
on the quiz will be con
Math 009 Quiz 1
Chapters 1 2
Dr. Cheryl Cleaves
Fall OL4 2017
Name Ronchelle S. Lathers
Instructions:
The quiz is worth 100 points. There are 10 problems, each worth 10 points. Your score
on the quiz
MATH 107 - 7983 Spring 2017 Quiz 3
Instructor: Rochelle Harley
Name_
I have completed this assignment myself, working independently and not consulting anyone
except the instructor. (Your signature is
MATH 107 - 7983 Spring 2017 Quiz 4
Instructor: Rochelle Harley
Name_
I have completed this assignment myself, working independently and not consulting anyone
except the instructor. (Your signature is
Sequences and Series of Functions
Pointwise and Uniform Convergence
Definition. Let (fn) be a sequence of functions defined on a subset S of R.
Then (fn) converges pointwise on S if for each x in S, t
Infinite Series (Week 7)
Definition. If | | converges, then the series converges is said to converge absolutely (or to be
absolutely convergent). If converges but | | diverges, then is said to co
Find the standard equation of the circle and then graph it.
5. Center (e,2), radius
The Standard Equation of a Circle: The equation of a circle with center (h,k) and radius r >0 is
( xh )2 + ( yk )2=
UMUC
Math 103
Final Exam Practice
You have two and a half hours to complete this exam.
The examination has 20 questions. (There are 5 more here for extra practice.)
This is a closed book, closed notes
Hefferon: Chapter 1 (pgs 1-77, skip 35-49)
Chapter One
Linear Systems
I Solving Linear Systems
Systems of linear equations are common in science and mathematics. These two
examples from high school sc
Math 240 Homework Assignment Three (W4) Solutions
1. [4] Show (that is, verify all the axioms) that the set of second degree polynomials
defined as,
! = = ! + + , ,
is a vector space. What is the dim
Math 240: Linear Algebra
Application Project: Hill Substitution Ciphers
Overview
This project introduces students to an encryption scheme called the Hill Substitution Cipher.
This encryption tec
QUIZ # 2 Solution Keys
Math 141/7980, Due 11:59PM, Sunday, April 2, 2017
1. (15 points) The area enclosed between = 2 and = 4 is revolved about the
horizontal line = 4 to form a solid. Calculate the v
QUIZ # 7 Solution Key
Math 141/7980, Due 11:59PM, Thursday, May 4, 2017
1. (10.6) Determine whether or not the alternating series converge or diverge.
(1) n
(a)
2
n 1 ln( n 1)
Solution:
1
(1) n
Let a
QUIZ # 1 Solution Keys
Math 141/7980, Due 11:59PM, Sunday, March 26, 2017
1. The velocity of a car after t seconds is 2 + 3 feet per second. (a) How far does the car
travel between = 4 second and = 10
Limits and Continuity
Limits of Functions
Definition. Let f: D R and let c be an accumulation point (cluster point) of D.
We say that a real number L is a limit of f at c, if
for each > 0 there exists
Sequences
Section 16: Convergence
(notes by S. Sands)
[Chapter 2 in Lebl]
* denotes a very important theorem!
Definitions.
A sequence is a function whose domain is the set N of natural numbers.
Notati
Sequences - Part 2 (Week 4)
Infinite Limits
Definition. A sequence (sn) is said to diverge to +
and we write lim (sn) = + provided that
for every M in R there exists a number N such that n > N implie
Topology of the Real Numbers ; Compact Sets
See Section 1.3 of Trench.
Definition: Let x R and let > 0. A neighborhood of x (or an -neighborhood of x) is a set of the form
N(x; ) = cfw_y R : |x - y| <
Relations and Functions
Cartesian product
Given two sets A and B, the Cartesian product of A and B, denoted A B (read "A cross
B"), is the set of all ordered pairs (a, b), where a is in A and b is in
Differentiation
(notes by S. Sands)
The Derivative
(Def. 4.1.1, Lebl, p. 131)
Definition: Let f: I R be a real-valued function defined on an interval I containing the point c.
(We allow the possibilit
Cardinality
Sets S and T have the same cardinality (are equinumerous), denoted S ~ T, if there exists a bijective
function from S onto T.
Given a collection of sets , ~ is an equivalence relation on .
Bounds, Supremum, Infimum, the Completeness Axiom, and the Archimedean Property
Section 12: The Completeness Axiom
Definitions. Let S be a subset of R.
If there exists a real number m such that m s fo
Natural Numbers and Induction
Natural Numbers
Peano Axioms: Suppose there exists a set P, whose elements are called natural numbers, having the
following properties.
P1. There exists a natural number,
Infinite Series (Week 6)
Convergence of Infinite Series
Summation notation
= +
+ +
Def. 2.5.1 Lebl, p. 72
Let (sn) be the sequence of partial sums defined by = = + + + .
If (sn) co
Ordered Fields
Assume the existence of a set R, called the set of real numbers, and two operations + and , called
addition and multiplication, such that the following properties apply:
Field Axioms
A1
Inequalities and Absolute Value
Theorem. Let x, y R. If x y + for every > 0, then x y.
Contrapositive: Let x, y R. If x > y, then x > y + for some > 0.
Note: "not x y" means "x > y" because of the tri
Mid-Term Exam/Week 4
MA115 Pre-Calculus
Instructor: Staci Gash
Instructions: This mid-term exam covers through week 4. You may either type your answers and submit
as a word doc or use pencil and paper
Math 009 Quiz 1
Professor: Tara Wells
Name: Traci Smith
Instructions:
The quiz is worth 50 points. There are 10 problems, each worth 5 points. Your score on
the quiz will be converted to a percentage
MATH 301 Week 6 Homework Solutions, Fall, 2017. Due Tuesday, October 24.
There are 9 problems, most with multiple parts.
The Derivative (#1-3, 21 points)
#1. Define f: R\cfw_0 R by
=
. Use the defi