Dear Penelope,
I am going to share with you an excerpt from my past. I would like to describe to you
what my life, as an Athenian, was like throughout the Peloponnesian War. The Athenian
government was considered a democracy. People had equal rights and l
Version A
1. Differentiate each of the following. (You may use derivative rules for these problems.)
f (x) = x9 4x5 + 5x2 1 f 0 (x) = 9x8 20x4 + 10x
3
1
g(x) = 4 x + x52 + 3 ln x= x 4 + 5x2 + 3 ln x; g 0 (x) = 41 x 4 10x3 +
3
x
2. Build a sign chart for
EXAM 1 STUDY GUIDE: KEY CONCEPTS AND IMPORTANT MATERIAL
Please study the material outlined here and be familiar with the relevant examples and exercises that we
went over in class
1.1 The Characteristics of Life
The science of biology is the study of livi
Version K
1. Find all absolute extrema of the function f (x) = x2 7x + 1 on the interval [0, 4].
f 0 (x) = 2x 7
Critical Numbers: x = 3.5
f (0) = 1
f (4) = 11
f (3.5) = 11.25
f has an absolute maximum of 1 at x = 0 and an absolute minimum of 11.25 at
x =
Version E
1. Find f 0 (x) if f (x) = 2xex . Simplify (fully factor) your answer.
f 0 (x) = 2xex + 2ex
= 2ex (x + 1)
2. Find f 0 (x) if f (x) =
ln x
.
3x
Simplify (fully factor/cancel) your answer.
3x
1
x
(ln x)(3)
(3x)2
3 3 ln x
=
9x2
1 ln x
=
3x2
3. Fi
Complete the following sentence: According to the Garden story in Genesis 2-3, a husband
rules over his wife because .
The man and the woman listened to the snake and disobeyed gods command.
Complete the following sentence: In Genesis 1-2, after almost ea
Review sheet for CRLS 1001 Exam 1
Following a thorough reading of Chapter 1 and lecture notes, students should be able to:
1. Discuss the relationship between terrorism and seven transnational crimes.
2. Explain the reach of criminology as a reflection of
Theology 1001
Sections 101111
Spring 2017
Worksheet for Friday, January 27
Your assignment is to note similarities and differences between Genesis 13 and Enuma Elish.
Please fill in the empty boxes in the table below and submit your completed work to the
Version J
1. The weekly pricedemand equation for a large pizza is
p = 38.8 0.002x
where x is the number of pizzas sold each week at a price of p dollars.
(a) Write the pricedemand equation in terms of price, i.e. find x = f (p).
p = 38.8 0.002x
0.002x = 3
Assyria, which comes from the ancient city of Ashur, began thriving around 675 B.C.
when they conquered Egypt. The great king, Sennacherib played a primary role in the uprising of
the Assyrian empire. At that time, I greatly enlarged the site of Nineveh.
MATH 4420 Class 1.
Chapter 1
We will touch on all the topics below, but (most of) your homework for Wednesday entails reading Chapter
1 and Section 2.1 thoroughly. I will ask you questions about them Wednesday.
1.1 Geometry before Euclid. What did it do?
MATH 4420 Class 3.
Chapter 2
Start with review of Incidence Geometry, the Parallel Postulates, and the Fano and Poincare disk models (or
at end of class). Homework if you havent done it already: spend some time reading 2.4 and 2.5 carefully.
Fanos geometr
IncidenceAxiom1. For every pair of distinct points P and Q there exists exactly one line L such that
both P and Q lie on L.
Incidence Axiom 2. For every line L there exist at least two distinct points P and Q such that both P
and Q lie on L.
Incidence Axi
MATH 4420
TEST 1
FALL 2016
Name:
All problems refer to Neutral Geometry (i.e. Chapter 3 geometry) unless otherwise specified.
1. Define the following terms (you dont have to repeat the book/notes definition verbatim, but the meaning
has to be identical):
MATH 4420 Class 2.
Chapter 2
2.1 Recap. An axiomatic system consists of undefined terms and axioms, together with definitions
and theorems.
An interpretation is an assignment of a specific meaning to the undefined terms. It is a model if
the axioms are tr
MATH 4420 Class 5.
Chapter 3
Recap:
Undefined terms: point, line, distance, half-plane, angle measure (and, later, area).
Axiom 3.1.1 (The Existence Postulate). The collection of all points forms a nonempty set. There is
more than one point in that set.
A
MATH 4420 Class 8.
Section 3.5. The Crossbar Theorem and the Linear Pair Theorem
From last time . Theorem 3.3.10 (betweenness definitions agree) said that, given three noncollinear points
A, B and C and a point D on the line BC, the point D is between B a
MATH 4420 Review Guide for Test 1.
Included with the test will be the list of undefined terms and axioms for Incidence Geometry and for the
geometry of Chapter 3 (i.e. Neutral Geometry, as well be calling it). But I expect you to be able to
clearly and a
MATH 4420 Class 4.
First well consider our final example of an incidence geometry: the Poincare disk (p.290 in book).
Chapter 3
Were going to start all over with a new set of axioms, for plane geometry, as a replacement for Euclids
Axioms. Incidence Geome
Some Chapter 3 solutions.
3.2.3 I believe you all got this (if not, see me this applies to all problems at this point).
3.2.12(a) Given f satisfies the conditions for being a coordinate function, show the same is true for f .
Show 11: suppose (f )(P ) =
Math 2451 Differential Equations
Spring 2017
Exam #1, Practice #1
1. (20 points) Consider the initial-value problem:
x
dy
+ y = 2x, y(1) = 1.
dx
(a) (15 points) Find the solution, y(x).
(b) (5 points) Find the largest interval for which your solution y(x)
Math 2451 Differential Equations
Spring 2017
Exam #1, Practice #3
1. (20 points) Solve
dy
5
5y = xy 3 .
dx
2
Solution: The equation is Bernoulli with n = 3. We use the substitution
u = y 13 = y 2 ,
dy
du
= 2y 3
dx
dx
Before we make the substitutions, we
Math 2451 Differential Equations
Spring 2017
Exam #1, Practice #2
1. (20 points) Find the general solution of the linear differential equation:
dy
y
= + xex .
dx
x
Solution: The equation is linear. The standard form is
1
dy
y = xex
dx x
so p(x) =
1
and
Math 2451 Differential Equations
Spring 2017
Exam #1, Practice #4
1. (20 points) Consider the initial value problem:
x5 + 5y 5 5xy 4
dy
= 0,
dx
y(1) = 1.
(a) Show that the differential equation is both homogeneous and Bernoulli.
(b) Find the solution.
Sol
Math 2451 Differential Equations
Spring 2017
Exam #1, Practice #2
1. (20 points) Find the general solution of the linear differential equation:
dy
y
= + xex .
dx
x
2. (20 points) Show that the following differential equation is exact. Then find the soluti
Math 2451 Differential Equations
Spring 2017
Exam #1, Practice #1
1. (20 points) Consider the initial-value problem:
x
dy
+ y = 2x, y(1) = 1.
dx
(a) (15 points) Find the solution, y(x).
(b) (5 points) Find the largest interval for which your solution y(x)
Math 2451 Differential Equations
Spring 2017
Exam #1, Practice #3
1. (20 points) Solve
dy
5
5y = xy 3 .
dx
2
2. (20 points) The following differential equation is linear, exact, and homogeneous:
(y x) dx + x dy = 0.
Solve it two different ways.
3. (20 po
Math 2451 Differential Equations
Spring 2017
Exam #1, Practice #4
1. (20 points) Consider the initial value problem:
x5 + 5y 5 5xy 4
dy
= 0,
dx
y(1) = 1.
(a) Show that the differential equation is both homogeneous and Bernoulli.
(b) Find the solution.
2.
4/9/2017
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1. See last exam notes
2.
Conservation biology understands human impacts on ecosystems, predicts future impacts,
changes unfavorable outcomes, restores species and habitats, and discovers new ways humans and
nature can coexist.
Research Cases
1. Invasive