College Algebra
Fifth Edition
James Stewart
Lothar Redlin
Saleem Watson
6
Systems of
Equations and
Inequalities
6.5
Systems of Inequalities
Systems of Inequalities
In this section, we study:
Systems of inequalities in two variables
from a graphical point
DIFFERENTIATION OF
EXPONENTIAL FUNCTIONS
OBJECTIVES:
apply the properties of exponential functions
to simplify differentiation;
differentiate functions involving exponential
functions; and
solve problems involving differentiation of
exponential functio
THE DERIVATIVE AND DIFFERENTIATION
OF ALGEBRAIC FUNCTIONS
OBJECTIVES:
to define the derivative of a function
to find the derivative of a function by
increment method (4step rule)
to identify the different rules of differentiation
and distinguish one from
DIFFERENTIATION OF
LOGARITHMIC
FUNCTIONS
OBJECTIVES:
differentiate and simplify logarithmic
functions using the properties of logarithm,
and
apply logarithmic differentiation for
complicated functions and functions with
variable base and exponent.
TRANS
DIFFERENTIATION OF
LOGARITHMIC
FUNCTIONS
OBJECTIVES:
differentiate and simplify logarithmic
functions using the properties of logarithm,
and
apply logarithmic differentiation for
complicated functions and functions with
variable base and exponent.
TRANS
THE DERIVATIVE AND DIFFERENTIATION
OF ALGEBRAIC FUNCTIONS
OBJECTIVES:
to define the derivative of a function
to find the derivative of a function by
increment method (4step rule)
to identify the different rules of differentiation
and distinguish one from
HIGHER ORDER DERIVATIVES
AND
IMPLICIT DIFFERENTIATION
OBJECTIVES:
to define higher derivatives;
to apply the knowledge of higher derivatives
and implicit differentiation in proving
relations;
to find the higher derivative of algebraic
functions; and
t
HIGHER ORDER DERIVATIVES
AND
IMPLICIT DIFFERENTIATION
OBJECTIVES:
to define higher derivatives;
to apply the knowledge of higher derivatives
and implicit differentiation in proving
relations;
to find the higher derivative of algebraic
functions; and
t
LIMITS
OF
FUNCTIONS
LIMITS OF FUNCTIONS
OBJECTIVES:
define limits;
illustrate limits and its theorems; and
evaluate limits applying the given
theorems.
define onesided limits
illustrate onesided limits
investigate the limit if it exist or not using
t
FUNCTIONS
OBJECTIVES:
define functions;
distinguish between dependent and
independent variables;
represent functions in different ways; and
evaluate functions
define domain and range of a function;
and
determine the domain and range of a
function
DEFINIT
LIMITS
OF
FUNCTIONS
INFINITE LIMITS; VERTICAL AND
HORIZONTAL ASYMPTOTES;
SQUEEZE THEOREM
OBJECTIVES:
define infinite limits;
illustrate the infinite limits ; and
use the theorems to evaluate the limits of
functions.
determine vertical and horizontal asymp
FUNCTIONS
GRAPHS OF FUNCTIONS; PIECEWISE
DEFINED FUNCTIONS; ABSOLUTE VALUE
FUNCTION; GREATEST INTEGER FUNCTION
OBJECTIVES:
sketch the graph of a function;
determine the domain and range of a
function from its graph; and
identify whether a relation is a
LIMITS
OF
FUNCTIONS
CONTINUITY
DEFINITION: CONTINUITY OF A FUNCTION
Definition 1.5.1 (p. 110)
If one or more of the above conditions fails to hold
at C the function is said to be discontinuous.
Theorem 1.5.3 (p. 113)
EXAMPLE
x2 x 6
1. Given the function f
DIFFERENTIATION OF
INVERSE TRIGONOMETRIC
FUNCTIONS
OBJECTIVES:
derive the formula for the derivatives of the
inverse trigonometric functions;
apply the derivative formulas to solve for the
derivatives of inverse trigonometric
functions; and
solve probl
Fundamental Counting Principles
Math104
Marie Louise G.
Biunas
FCP
Fundamental Counting Principles
Total possible outcomes of
compound events is found by
multiplying the number of outcomes
for each event
Example
#1
You flip a coin and spin the spinner. H
MAPA INSTITUTE OF TECHNOLOGY
Department of Mathematics
a.
b.
c.
1.
2.
VISION
Mapua shall be among the best universities in the world.
MISSION
The Institute shall provide a learning environment in order for its students to acquire the attributes
that will
Siy, Vince Roosevelt
CE1
2014107357
PROTOCOLS

Attendance will be done with proper identification card
Be briefed about the activity and the community to be visited that day.
Be paired into groups to be safer and be more organized
Be given the materials
Macalalad, Isaac Jerone S.
2014103892
4
CE1
CWTS02B16
Assignment No.
As we all know, all living organisms are living in this planet, the Earth. Because we are living
in this planet, we have the responsibility to take care of it. We, humans, can make thi
BREAKING THE TAPE METHOD
L= FULL LENGTH OF THE TAPE
L
L
L
L
L1=PARTIAL LENGTH
OF THE TAPE
ABNEY HAND LEVEL AND TAPE METHOD
HD1
1
HD2
SD1
A
2
HD3
A
SD2
3
a
SD3
b
B
Mapua Institute of Technology
ELEMENTARY SURVEYING
FIELD WORK NO. 4
DETERMINING THE AREA OF A
POLYGONAL FIELD USING ONL THE
SLOPE
COURSE AND SECTION: CE1200F/B2
SUMBMITTED BY:
BIUNAS, MARIE LOUISE G.
STUDENT NO. 2014106065
GROUP NO. 3
Date of Field Work:
FIELD WORK PEER ASSESSMENT
COURSE: CE1200F
SECTION: B2
DATE: OCTOBER 22, 2015
FIELDWORK TITLE: DETERMINING THE AREA OF A POLYGONAL FIELD USING THE TAPE
GROUP MEMBERS:
GROUP NO. 3
2. DATU, CHRISTINE
3. PASTRANA, MICAH
4. SUCGANG, JENBERT
CRITERIA
1. STO.
DIFFERENTIATION OF
EXPONENTIAL FUNCTIONS
OBJECTIVES:
apply the properties of exponential functions
to simplify differentiation;
differentiate functions involving exponential
functions; and
solve problems involving differentiation of
exponential functio
FUNCTIONS
OPERATIONS ON FUNCTIONS
OBJECTIVES:
perform operations on functions;
determine the domain of the given functions;
determine the domain of the resulting functions
after performing the operations on functions; and
define a composite function a
CO2
Math211
Distinguish equations representing the
circles and the conics; use the properties
of a particular geometry to sketch the
graph in using the rectangular or the polar
coordinate system. Furthermore, to be
able to write the equation and to solve
CO3
Discuss and apply comprehensively the concepts, properties
and theorems of functions, limits, continuity and the
derivatives in determining the derivatives of algebraic
functions
COVERAGE
Limits:
Definition and Concepts
Theorems OneSided Limits
Limit