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VOTERS EDUCATION MANUAL
(Note: the topics and the discussions are in the manual given)
9:00 9:30
MODULE 1: ENGAGED CITIZENSHIP
OBJECTIVES:
At the end of the module, the participants must be able to:
a. Understand that their situations become part of the b
Esnea Jane O. Delos Reyes
Math 203 | 7034 | BE 222
1. History of the Integral from the 17th Century
1.1 Introduction
The path to the development of the integral is a branching one, where similar discoveries were made
simultaneously by different people. Th
Esnea Jane O. Delos Reyes
Math 203 | 7034 | BE 222
History of Integral Calculus
Pre-calculus integration
The first documented systematic technique capable of determining integrals is the method of
exhaustion of the ancient Greek astronomer Eudoxus (ca. 37
Integral calculus
The branch of mathematics in which the notion of an integral, its properties and methods of
calculation are studied. Integral calculus is intimately related to differential calculus, and
together with it constitutes the foundation of mat
(Math)
triangle = (1/2) b h
(pi = = 3.141592.)
Areas
square = a
equilateral triangle = (1/4) (3) a2
triangle given SAS = (1/2) a b sin C
2
rectangle = ab
parallelogram = bh
trapezoid = h/2 (b1 + b2)
cylinder = b h = r2 h
triangle given a,b,c = [s(s-a)(s-b
ALGEBRA 1
Man-hours (is always assumed constant)
LOGARITHM
(Wor ker s1 )(time1 ) (Wor ker s 2 )(time2 )
=
quantity.of .work1
quantity.of .work 2
x = log b N N = b x
Properties
ALGEBRA 2
log( xy ) = log x + log y
x
log = log x log y
y
log x n = n log x
Limits Indeterminate Forms and LHospitals Rule
I. Indeterminate Form of the Type
0
0
We have previously studied limits with the indeterminate form
0
as shown in the
0
following examples:
x2 4
( x 2)( x 2)
lim
lim x 2 2 2 4
x 2
x 2
x 2
x 2
Example 1: lim
x
Time Rates | Applications
Time Rates
If a quantity x is a function of time t, the time rate of change of x is given by dx/dt.
When two or more quantities, all functions of t, are related by an equation, the relation between
their rates of change may be ob
Chapter4TrigonometricandInverseTrigonometric
Functions
Differentiation of Trigonometric Functions
Trigonometric identities and formulas are basic requirements for this section. If u is a
function of x, then
1.
2.
3.
4.
5.
6.
Differentiation of Inverse Tri
FOLLOW UP
COMMITTEE FOR BM
ACCOUNTANCY
Name
Alyssa Faye Abanilla
Christian Mae Barcoma
Kristine Buenaflor
Samantha Rae Camia
Mel Dioso
Hosnie Mutin
Ferdauza Jane Mustapha
Contact Number
E-mail Address
09103085970
09065086535
09214829069
09303821089
afraba
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The HALOGENS OR HALOGEN ELEMENTS are a series
ofnonmetalelementsfromgroup17oftheperiodictable(formerly:
VII,VIIA),comprisingfluorine(F),chlorine(Cl),bromine(Br),iodine
(I),andastatine(At).
The group of halogens is the only periodic table group which
conta
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Time t
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