Application of definite integrals,we will explore some of the many application of definite integral by using it to calculate areas between two curves, volumes, length of curves, and several other application.
Application of definite integrals,we will explore some of the many application of definite integral by using it to calculate areas between two curves, volumes, length of curves, and several other application.
A circle is a simple shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the center; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant.
Business Mathematics ( 1st and 2nd years )immanuel66
Its is concerned with use of MATHS in BUSINESS. This ppt tells about use of mathematical tool like linear programming, calculus, probability,linear equation.
(a) Natural Numbers : N = {1,2,3,4,...}
(b) Whole Numbers : W = {0,1,2,3,4, }
(c) Integer Numbers :
or Z = {...–3,–2,–1, 0,1,2,3, },
Z+ = {1,2,3,....}, Z– = {–1,–2,–3, }
Z0 = {± 1, ± 2, ± 3, }
(d) Rational Numbers :
p
Q = { q ; p, q z, q 0 }
(i) R0 : all real numbers except 0 (Zero).
(j) Imaginary Numbers : C = {i,, }
(k) Prime Numbers :
These are the natural numbers greater than 1 which is divisible by 1 and itself only, called prime numbers.
Ex. 2,3,5,7,11,13,17,19,23,29,31,37,41,...
(l) Even Numbers : E = {0,2,4,6, }
(m) Odd Numbers : O = {1,3,5,7, }
Ex. {1,
Note :
5
, –10, 105,
3
22 20
7 , 3
, 0 ....}
The set of the numbers between any two real numbers is called interval.
(a) Close Interval :
(i) In rational numbers the digits are repeated after decimal.
(ii) 0 (zero) is a rational number.
(e) Irrational numbers: The numbers which are not rational or which can not be written in the form of p/q ,called irrational numbers
Ex. { , ,21/3, 51/4, ,e, }
Note:
(i) In irrational numbers, digits are not repeated after decimal.
(ii) and e are called special irrational quantities.
(iii) is neither a rational number nor a irrational number.
(f) Real Numbers : {x, where x is rational and irrational number}
20
[a,b] = { x, a x b }
(b) Open Interval:
(a, b) or ]a, b[ = { x, a < x < b }
(c) Semi open or semi close interval:
[a,b[ or [a,b) = {x; a x < b}
]a,b] or (a,b] = {x ; a < x b}
Let A and B be two given sets and if each element a A is associated with a unique element b B under a rule f , then this relation is called function.
Here b, is called the image of a and a is called the pre- image of b under f.
Note :
(i) Every element of A should be associated with
Ex. R = { 1,1000, 20/6, ,
, –10, –
,.....}
3
B but vice-versa is not essential.
(g) Positive Real Numbers: R+ = (0,)
(h) Negative Real Numbers : R– = (– ,0)
(ii) Every element of A should be associated with a unique (one and only one) element of but
any element of B can have two or more rela- tions in A.
3.1 Representation of Function :
It can be done by three methods :
(a) By Mapping
(b) By Algebraic Method
(c) In the form of Ordered pairs
(A) Mapping :
It shows the graphical aspect of the relation of the elements of A with the elements of B .
Ex. f1:
f2 :
f3 :
f4 :
In the above given mappings rule f1 and f2
shows a function because each element of A is
associated with a unique element of B. Whereas
f3 and f4 are not function because in f 3, element c is associated with two elements of B, and in f4 , b is not associated with any element
of B, which do not follow the definition of function. In f2, c and d are associated with same element, still it obeys the rule of definition of function because it does not tell that every element of A should be associated with different elements of B.
(B) Algebraic Method :
It shows the relation between the elem
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
1. Functions & Graphs by Mrs. Sujata Tapare Prof. Ramkrishna More A.C.S. College, Akurdi
2.
3. Function terminology R Z f 4.3 4 Domain Co-domain Pre-image of 4 Image of 4.3 f maps R to Z f(4.3)
4. Even more functions Not a function Range 1 2 3 4 5 “ a” “ bb“ “ cccc” “ dd” “ e” 1 2 3 4 5 a e i o u It is a function
5.
6. 5 5 0 -2 Constant function: f(x) = 5 Rational function: f(x) = (4- x 2 )/(x+2) Polynomial function: f(x) = x 2 Identity function: f(x) = x
7.
8.
9. One-one functions Function f : R -> R is one-one for any x, y Є R, f(x) = f(y) x = y. Examples Let f:R R defined by, f(x) = 3x – 2 f(x)= f(y) 3x – 2 = 3y – 2 x = y Thus, f(x) is one-one Let f:R R defined by, f(x) = 3x 2 – 2 f(x)= f(y) 3x 2 –2= 3y 2 –2 3x 2 = 3y 2 x = ± y Thus, f(x) is not one-one
![What of a function? ,[object Object],[object Object],[object Object],[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)