Procedures and Problem Solving
Equality of Complex Numbers In Exercises 710, nd
real numbers a and b such that the equation is true.
38. ( + Ji)(f J31) 32/51. .4
40. (5 4i)2 (54%9'9 55-351 t?-
10. (a+6)+2bi=6i
Writing a Complex Number in Standard Form In
MAC2311 Additional Exercises from Larson, Calculus Early Transcendental Functions
(Note: It is highly recommended that you purchase the Complete Solutions Manual, Vol. 1 to
accompany the text. If you have the manual, also attempt the even numbered exercis
HOW HAS PAINTING CHANGED YOUR LIFE?
Name: Tran Minh Nguyet Course: Public speaking Professor: Nguyen Thi Thuy Huong
1. PSYCHOLOGY
Painting washes
from the soul
the dust of everyday
life
MEDITATION
2. INSPIRATION
Vila Cruzeiro
Notorious slum becomes open-a
WELCOME TO OUR PRESENTATION
Course: Introductio to Public Speaking
Professor: Dr. Nguen Thi Thuy Huong
Functions of Year round air
conditioning
Heating and humidification of air in winter
Cooling and dehumidification in summer
Why should we choose SHARP
SPEECH WORKSHOP
Evaluating a Peakers Rhetorical Effectiveness.
I decide to choose this talk of Larry Smith from TED to clarify the following
questions.
https:/www.ted.com/talks/larry_smith_why_you_will_fail_to_have_a_great_caree
r?language=en
1. Speech Go
WELCOME TO OUR
PRESENTATION
How to be a good public speaker
DEREK SIVERS
Course: Introduction to Public Speaking
Professor: Dr.Nguyen Thi Thuy Huong
Derek Sivers
an American
entrepreneur
best known for being
the founder and former
president of CD Baby,
Integration:
1. Income distribution: the coefficient of inequality for each Lorentz curve
1
Integration. L=2
[xf ( x )]dx
0
the lower result will be more equitable
income distribution.
2. Sinking funds: how much money need to establish the fund to with
1
Preliminaries
Precalculus Review I
Precalculus Review II
The Cartesian Coordinate System
Straight Lines
1.1
Precalculus Review I
The Real Number Line
We can represent real numbers geometrically by points on
a real number, or coordinate, line:
Origi
3
Differentiation
Basic Rules of Differentiation
The Product and Quotient Rules
The Chain Rule
Marginal Functions in Economics
Higher Order Derivatives
3.1
Basic Rules of Differentiation
1.
2.
3.
4.
Derivative of a Constant
The Power Rule
Derivative
5
Exponential and Logarithmic Functions
Exponential Functions
Logarithmic Functions
Compound Interest
Differentiation of Exponential Functions
Exponential Functions as Mathematical Models
5.1
Exponential Functions
Exponential Function
The function d
6
Integration
Antiderivatives and the Rules of Integration
Integration by Substitution
Area and the Definite Integral
The Fundamental Theorem of Calculus
Evaluating Definite Integrals
Area Between Two Curves
Applications of the Definite Integral to
Precalculus
Wkst- Linear Functions and Linear Modeling
Name:_
Date:_
1. A town's population has been growing linearly. In 2003, the population was 45,000, and the population has
been growing by 1700 people each year.
a. Write an equation, P t , for the po
HW 1.2.1: Function Foundations (Domain and Range)
Inequality
5 h 10
Set Builder Notation
h | 5 h 10
Interval notation
(5, 10]
5 h 10
h | 5 h 10
h | 5 h 10
h | h 10
h | h 10
h| h
[5, 10)
5 h 10
h 10
h 10
all real numbers
(5, 10)
( ,10)
[10, )
( , )
8.4 day one
Improper Integrals
Greg Kelly, Hanford High School, Richland, Washington
Until now we have been finding integrals of continuous functions over closed intervals.
Sometimes we can find integrals for functions where the function or the limits are
8.3 Relative Rates of Growth
Greg Kelly, Hanford High School, Richland, Washington
y = e x grows very fast. The function
We could graph it on the chalkboard: If x is 3 inches, y is about 20 inches:
( 3, 20 )
Wte64 inches, the y-value We have gone less tha
8.2 Day 2: Identifying Indeterminate Forms
Photo by Vickie Kelly, 2008
Brooklyn Bridge, New York City
Greg Kelly, Hanford High School, Richland, Washington
What makes an expression indeterminate?
Consider:
We can hold one part of the expression constant
8.2 day 1 LHpitals Rule
Actually, LHpitals Rule was developed by his teacher Johann Bernoulli. De lHpital paid Bernoulli for private lessons, and then published the first Calculus book based on those lessons.
Guillaume De l'Hpital 1661 - 1704
Greg Kelly,
8.1: Sequences
Craters of the Moon National Park, Idaho
Photo by Vickie Kelly, 2008 Greg Kelly, Hanford High School, Richland, Washington
A sequence is a list of numbers written in an explicit order.
cfw_ an = cfw_ a1, a2 , a3, . , an , .
nth term
Any r
Chapter 7 Extra Topics
Crater Lake, Oregon
Photo by Vickie Kelly, 1998 Greg Kelly, Hanford High School, Richland, Washington
Centers of Mass:
Fg
d
Take Superior, Washburn, WI L orque is a function of force and distance. Photo by Vickie Kelly, 2004 (Torque
7.5 Fluid Pressure and Forces
Georgia Aquarium, Atlanta
Photo by Vickie Kelly, 2006 Greg Kelly, Hanford High School, Richland, Washington
What is the force on the bottom of the aquarium? 2 ft
Force = weight of water = density volume
lb = 62.5 3 2 ft 3 ft
Hoover Dam Nevada & Arizona
Photo by Vickie Kelly, 2004
7.5 part 1 Work and Pumping Liquids
Greg Kelly, Hanford High School, Richland, Washington
Hoover Dam Powerhouse Nevada & Arizona
Photo by Vickie Kelly, 2004 Greg Kelly, Hanford High School, Richland,
A.P Calculus Worksheet: Areas of Surfaces of Revolution
Find the areas of the surfaces generated by revolving the curves in problems 1-4 about the axes indicated: 1. y = x / 2, 0 x 4 , about the x -axis. Check your result with a formula from geometry. 2.