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
Home
Courses
Calendar
Personal
You are here
adnuhs.portal
/ WEB201A
/ Quizzes
/ Quiz_8/14*
/ Review of attempt 1
Quiz_8/14*
Review of attempt 1
Finish review
Started on
Tuesday, 14 August 2012, 10:53 AM
Completed on Tuesday, 14 August 2012, 10:58 AM
Time
Home
Courses
Calendar
Personal
You are here
adnuhs.portal
/ WEB201A
/ Quizzes
/ C2_Quiz 8-02_Honors Class
/ Review of attempt 1
C2_Quiz 8-02_Honors Class
Review of attempt 1
Finish review
Started on
Friday, 3 August 2012, 10:58 AM
Completed on Friday, 3
Home
Courses
Calendar
Personal
You are here
adnuhs.portal
/ WEB201A
/ Quizzes
/ C2_Quiz7-27*
/ Review of attempt 1
C2_Quiz7-27*
Review of attempt 1
Finish review
Started on
Friday, 27 July 2012, 10:28 AM
Completed on Friday, 27 July 2012, 10:29 AM
Time t
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
Home
Courses
Calendar
Personal
You are here
adnuhs.portal
/ WEB201A
/ Quizzes
/ E_Quiz_June 16
/ Review of attempt 1
E_Quiz_June 16
Review of attempt 1
Finish review
Started on
Saturday, 16 June 2012, 03:49 PM
Completed on Saturday, 16 June 2012, 03:51 P
Home
Courses
Calendar
Personal
You are here
adnuhs.portal
/ WEB201A
/ Quizzes
/ E_Quiz_June Honors Class
/ Review of attempt 1
E_Quiz_June Honors Class
Review of attempt 1
Finish review
Started on
Friday, 22 June 2012, 10:28 AM
Completed on Friday, 22 Ju
Home
Courses
Calendar
Personal
You are here
adnuhs.portal
/ WEB201A
/ Quizzes
/ E_Quiz_June 26 Honors Class
/ Review of attempt 1
E_Quiz_June 26 Honors Class
Review of attempt 1
Finish review
Started on
Tuesday, 26 June 2012, 10:37 AM
Completed on Tuesda
Home
Courses
Calendar
Personal
You are here
adnuhs.portal
/ WEB201A
/ Quizzes
/ C1_Quiz_July 2
/ Review of attempt 1
C1_Quiz_July 2
Review of attempt 1
Finish review
Started on
Tuesday, 3 July 2012, 10:32 AM
Completed on Tuesday, 3 July 2012, 10:34 AM
Ti
Home
Courses
Calendar
Personal
You are here
adnuhs.portal
/ WEB201A
/ Quizzes
/ C1_Static and Dynamic Quiz_Honors Class
/ Review of attempt 1
C1_Static and Dynamic Quiz_Honors Class
Review of attempt 1
Finish review
Started on
Friday, 29 June 2012, 10:38
Home
Courses
Calendar
Personal
You are here
adnuhs.portal
/ WEB201A
/ Quizzes
/ C2_Quiz7-26_Honors Class
/ Review of attempt 1
C2_Quiz7-26_Honors Class
Review of attempt 1
Finish review
Started on
Thursday, 26 July 2012, 10:44 AM
Completed on Thursday, 2
Home
Courses
Calendar
Personal
You are here
adnuhs.portal
/ WEB201A
/ Quizzes
/ C1_Quiz_July 6_Honors Class
/ Review of attempt 1
C1_Quiz_July 6_Honors Class
Review of attempt 1
Finish review
Started on
Friday, 6 July 2012, 10:57 AM
Completed on Friday,