190
Chapter 9 Applications of Integration
It is clear from the gure that the area we want is the area under f minus the area
under g, which is to say
9
1
2
2
2
g(x) dx =
f (x) dx
1
1
f (x) g(x) dx.
It doesnt matter whether we compute the two integrals on

SJ10103
10/3/2014
Definition of market equilibrium
Equilibrium price and output
Market equilibrium is a situation where
quantity demanded and quantity
supplied are equal and there is no
price or quantity to change.
Market equilibrium is determined by the

12/8/2014
3.Areabetween2Curves
interactivemathematics
Learnmathbyplayingwithit!
Home
ApplicationsofIntegration
3.AreaBetween2Curves
3.AreaBetween2Curves
byM.Bourne
Wearetryingtofindtheareabetween2curves,y
f x andy
f x ,andthelinesx
aandx
b.
Weseethatifwes

SJ10103
9/22/2014
Definition of DEMAND
DD schedule and DD curve
Demand is defined as the ability and willingness to buy specific
Demand Schedule
quantities of goods in a given period of time at a particular price,
ceteris paribus.
Price
Quantity
9.0
2
8.5

Calculus I
Notes on Limits and Continuity.
Limitsofpiecewisefunctions:
Example#1: Consider the graph of the following piece-wise function. What is happening at or around 2?
x2 , x < 2
f (x ) = 7
,x = 2
3 x , x > 2
There are 3 things happening at or aroun

Logic
(Chapter 1 - Part 1)
Dr Hjh Noraini Abdullah
Faculty of Science and Natural Resources
LEARNING OUTCOMES
At the end of this chapter, you should be able to :
know
what logic is about
define some basic terminologies in logic
determine if a statement

Limit and Continuity
MODULE - V
Calculus
20
Notes
LIMIT AND CONTINUITY
Consider the function f(x) =
x2 1
x 1
You can see that the function f(x) is not defined at x = 1 as x 1 is in the denominator. Take the
value of x very nearly equal to but not equal to

Replacement class: 10/10/2014
BK2
8AM-9AM MICROECONOMICS I
PRACTICE QUESTIONS
Q1.
Show in diagram the effect on the demand curve, the supply curve, the
equilibrium price and the equilibrium quantity of each of the following events.
1a) The market for news

MATH0201 BASIC CALCULUS
MATH0201 BASIC CALCULUS
Venn Diagram and Subset Relation
MATH0201
BASIC CALCULUS
Set Operations
Set
Sample Space
Dr. WONG Chi Wing
Department of Mathematics, HKU
General Sets
Set Builder Notation
Some Examples
MATH0201 BASIC CALCUL

10/8/2014
Truth Table Solutions
Solutions to Truth Table Problems
These are the solutions to the truth table exercises. You are strongly advised to work out your own
solutions before you look at these.
1. Generate a truth table for the following statement

MQA 02-SM10103
1.
2.
3.
4.
Semester I Session 2014-2015
Table 3: Summary of information on each course SM10103
Name of Course:
Mathematics I
Course Code:
SM10103
Name(s) of academic staff: Dr.Hjh Noraini Abdullah
Rationale for the inclusion of the course/

10/30/2014
Domain and Range of a Function
interactive mathematics
Learn math by playing with it!
Home
Functions and Graphs
4a. Domain and Range of a Function
Domain and Range of a Function
Domain
The domain of a function is the complete set of possible

ME Direct Senior-Junior List
No
.
Name
Email
Senior name
Contact
Number
1
Alia Aqilah Binti Shafie
aliaaqilahshafie@gmail.com
010590924
6
2
Descey Binti Jurin
descey.jurin@yahoo
Syarifah
Khairunnisa
Syaierah
Binti
Wan
Raduan
Siti Nur Hasliza
3
Brenda Bene

10/30/2014
9. Even and Odd Functions
interactive mathematics
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Functions and Graphs
9. Even and Odd Functions
9. Even and Odd Functions
By M. Bourne
Even Functions
A function
= ( ) is said to be even if
( )= ( )
for all

*Please write up ONLY the final answer.
No need to show your calculation. Due
DATE 12/12/14 before 00:00 AM.
NAME:
MATRIC NUM:
PROGRAMME:
Exercises - Area
Example
1. Find the area of the finite region bounded by the curves
ANS:
2. Find the area of the fin

Limits
Continuity
Derivative
Calculus for the Life Sciences I
Lecture Notes Limits, Continuity, and the Derivative
Joseph M. Mahay,
mahaffy@math.sdsu.edu
Department of Mathematics and Statistics
Dynamical Systems Group
Computational Sciences Research Cent

HYPERBOLIC FUNCTIONS
Stan Wagon riding his tricycle with square wheels
(a mathematician at Macalester College in St. Paul)
HYPERBOLIC FUNCTIONS
Definitions
and
Identities
HYPERBOLIC FUNCTIONS
x
e e
cosh( x)
2
x
x
e e
sinh( x)
2
x
We pronounce
cosh(x)
si

SYSTEM OF REAL
NUMBER
(Chapter 1 Part 3)
Dr Hjh Noraini Abdullah
Faculty of Science and Natural
Resources
In this chapter, you will
define
number systems based on
those numbers that anyone is
familiar with: the natural numbers.
define - the 'real number

10/8/2014
Discrete Mathematics/Set theory/Answers - Wikibooks, open books for an open world
Discrete Mathematics/Set theory/Answers
Contents
1 Answers to Set Theory Exercise 1
2 Answers to Set Theory Exercise 2
3 Answers to Set Theory Exercise 3
4 Answers

10/30/2014
3. Graphical Representation of Complex Numbers
interactive mathematics
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Home
Complex Numbers
3. Graphical Representation
3. Graphical Representation of Complex Numbers
by M. Bourne
We can represent complex number

10/8/2014
Discrete Mathematics/Set theory/Exercises - Wikibooks, open books for an open world
Discrete Mathematics/Set theory/Exercises
Contents
1 Set Theory Exercise 1
2 Set Theory Exercise 2
3 Set Theory Exercise 3
4 Set Theory Exercise 4
5 Set Theory E

SJ10103
10/18/2014
Definition to elasticity
Elasticity measures the magnitude of responsiveness
of any variable to a change in one of the determinants
factors.
Formula of elasticity
The value of elasticity can be
measured by:
Elasticity , E =
For example

Logarithm and Exponential
Functions
Overview of logs and exponential functions
Logarithm is an exponent
Inverse functions
Log functions and exponential functions are
inverses of one another
Properties of logarithms
Logarithms/exponentials in scientific

Logic and Truth Tables
What is a Truth Table?
A truth table is a tool that helps you analyze statements or arguments in order to verify
whether or not they are logical, or true. There are five basic operations that you will utilize
when creating a truth t

Set Theory
(Chapter 1 Part 2)
Dr Hjh Noraini Abdullah
Faculty of Science and Natural Resources
In this chapter, you will
learn
the basic terms and facts about sets
see how sets can be combined to yield other sets.
LEARNING OUTCOMES
At the end of this chap

COMPLEX NUMBER
(Chapter 1 Part 4)
Dr Hjh Noraini Abdullah
Faculty of Science and Natural Resources
In this chapter, you will
see
how the real number system is only a
part of a larger number system; call the
"complex" numbers.
see how the interpretations

2.1 Introduction-Functions and Inverses
A function is a rule that assigns a unique value to every member in
its domain.
3
2
9
3
5
1 7
0
f
Notation: f (2) = 1, f (3) = 7, f (5) = 3 and f (9) =0
f consists of ordered pairs (2,1) (3, 7) (5, 3) (9, 0)
3
2
9
3