Math 180
Lecture Notes
Chapter Three
CHAPTER THREE: DIFFERENTIATION RULES
Section 3.1: Derivatives of Polynomials and Exponential Functions
f ( x h) f ( x )
) which
h 0
h
quickly became rather cumbersome. Our next task is to come up with rules of differen
Math 180
CHAPTER 5 REVIEW
1.
Given f ( x ) cos x 2 and the interval 0,2 use L4 (four rectangles, with left endpoints) to estimate the area
under f over the interval. Include a sketch.
2.
Let f ( x ) 3 x 9. Find the area under the curve on the interval 1,3
Math 180
Lecture Notes
Chapter Five
CHAPTER FIVE: INTEGRALS
Section 5.1: Areas and Distances
Two big questions led to the development of calculus. One was the question of how to find a tangent
line to a curve at a point. We approached this by approximatin
Math 180
Lecture Notes
Chapter Two
CHAPTER TWO: LIMITS AND DERIVATIVES
Section 2.1: The Tangent and Velocity Problems
Calculus was developed in response to problems and questions. Among these were the tangent and
velocity problems. Lets start with the tan
Math 180
Lecture Notes
Chapter One
CHAPTER ONE: FUNCTIONS AND MODELS
Selected Topics from Chapter One
Much of calculus is the study of functions, so we must be sure we have a solid understanding of
functions before we begin.
Functions can be thought of, a
Math 180
Lecture Notes
Chapter Four
CHAPTER FOUR: APPLICATIONS OF DIFFERENTIATION
Section 4.1: Maximum and Minimum Values
One of the most common applications of derivatives is optimization. In these problems we are trying to
find the best solutions. It ma
Orange Coast College
Business, Computing, & Career Education Division
CS/CIS Department
CS A170 (Java Programming )
Homework 11 - Survey
Instructor: Martha Malaty
CS 170 Homework 11 Assignment
Survey
Question
1. Which topic (or topics) did you like
the mo
Math 180
FINAL EXAM REVIEW
1.
Find the limits:
a.
c.
e.
g.
lim
x 5
lim
x5
x 5
b.
x 2 5 x 24
x 3
lim
x
d.
x2 9
3x 4
f.
4x 1
2
4 sin5 x cos 3 x
x 0
6x
h.
lim
Use the Squeeze Theorem to prove lim
3.
Show that x 5 2 x 4 x 3 0 has a root in (2,3).
4.
5.
lim
4
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"We have to deal with the 11 million (over 300 million ~ 3.6%) individuals
who are here illegally. We all agree that these men and women should have
to earn their way to citizenship. But for comprehensive immigration reform
to w
Math 180
CHAPTER 6 REVIEW
3
1.
Find the area under f ( x )
2.
Find the area of the shaded region, bounded by y cos x, y sec 2 x and x 4 .
3.
Find the area of the region bounded by y 3 sin x, y
4.
a.
Use disks to find the volume of the solid generated by
Math 180
Lecture Notes
Chapter Six
CHAPTER SIX: APPLICATIONS OF INTEGRATION
Section 6.1: Areas Between Curves
Recall how we first determined the value of a definite integral:
In this chapter, as we consider applications, we will continually return to this
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We have to deal with the 11 million (over 300 million ~ 3.6%)
individuals who are here illegally. We all agree that these men and
women should have to earn their way to citizenship. Weve got to lay
out a path a pro
Chapter 4: Civil Liberties: Protecting Individual Rights
Antoine Jones was arrested for dealing drug by having a tracking device installed in
his car by the police. Wrong according to Bill of Rights 4.
Our Individual Rights = Are complex and political by
Political Participation: is an involvement in activities designed and intended to influence public
policy and leadership, such as voting, joining political groups, and writing letters to elected
officials, demonstrating for politicals causes, and giving m
CHAPTER 6:
This chapter discusses Public Opinion and tis influence on the US political system.
A major theme is that public opinion is a powerful, not yet exact force , in American
politics.
The policies of the US Gov cannot be understood apart from publi
Politics L the means wby which society settles
Politics and power in America:
It is out nations / peoples cultural ideals that help to shape what people expect
from politics and inspire people to work together for a collective purpose!
Politics: Theo proc
Chapter 3: Federalism
Nature of the relationship between:
A- The National (Fed Gov)
B- The States (States Rights)
C- The Local Government (Establish local laws)
Federal Constitution
State Constitution
Local law by city council
This was the most pressing i
Constitutional Democracy Promoting Liberty and self-government
Blue-scantron
The president can appoint two judges, third judge has to be approved by the senate.
Main points to review
(Bill of right is the only in constitution protect personal rights)
Deve
(Chapter 8) Political Parties, Candidates and Campaigns
To win electoral majority, candidates of the two major parties must appeal to a diverse set of
interests; this nescessity normally leads them to advocate moderate and somewhat overlapping
policies.
O
Chapter 5:
Civil Rights vs Equal Rights: equal protection under the law.
Exam: 13,14,15th Amendment:
1. 13th: abolished slavery and conditions of involuntary servitude
2. 14th Amendment (1868): Prohibits state action denying any person the equal
protectio
Chap 11: Congress
Congress = House of Reps (435 members) + The Senate (100 members)
Together = The Congress = 535
At times, Congress takes the lead on broad national issues, but ordinarily it does not do so
Congresss policy-making role is based on 4 majo
Chap 12: Presidency
Exam:
Caucuses
Pg. 208 Top How dominate elect president.
Nomination 307
Unit rule 311 538 electoral college vote (270 votes)!
Pasge 333 (unit rule)
Staffing the Presidency !
EOP = National Seciruty white house office, Council of Ecnomi
Chap 10:
TEST
Four roles of media: Signaling, watchdog, common-carrier, partisan
Presses tied to nations political party system (P247) 3 stages: Partisan press, Yellow
journalism, and objective press).
Journalistic orientation open ideas and opinions
Trad