The document discusses the concept of limits. It explains that as the number of sides of a polygon increases, the area of the polygon approximates the area of the circle it is inscribed in, and the limit of the polygon's area is equal to the area of the circle. It also examines the limit of a function as x approaches 2 from both sides, and defines some fundamental rules of limits, such as the constant rule, sum rule, and multiplication rule. Finally, it outlines several techniques that can be used to calculate limits, including direct substitution, factoring, rationalization, and limits involving infinity and trigonometric, exponential and two-sided limits.
Continuity says that the limit of a function at a point equals the value of the function at that point, or, that small changes in the input give only small changes in output. This has important implications, such as the Intermediate Value Theorem.
The concept of limit formalizes the notion of closeness of the function values to a certain value "near" a certain point. Limits behave well with respect to arithmetic--usually. Division by zero is always a problem, and we can't make conclusions about nonexistent limits!
Lecture Presentation on Trigonometry, types of angle, angle measurement, pythagorean theorem, trigonometric function, trigonometric relationship, circle function, co function, reference angle, odd even function,graphing of trigonometric function, special angles and terminology and history of trigonometry
Continuity says that the limit of a function at a point equals the value of the function at that point, or, that small changes in the input give only small changes in output. This has important implications, such as the Intermediate Value Theorem.
The concept of limit formalizes the notion of closeness of the function values to a certain value "near" a certain point. Limits behave well with respect to arithmetic--usually. Division by zero is always a problem, and we can't make conclusions about nonexistent limits!
Lecture Presentation on Trigonometry, types of angle, angle measurement, pythagorean theorem, trigonometric function, trigonometric relationship, circle function, co function, reference angle, odd even function,graphing of trigonometric function, special angles and terminology and history of trigonometry
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Mat 121-Limits education tutorial 22 I.pdfyavig57063
limitsExample: A function C=f(d) gives the number of classes
C, a student takes in a day, d of the week. What does
f(Monday)=4 mean?
Solution. From f(Monday)=4, we see that the input day
is Monday while the output value, number of courses is
4. Thus, the student takes 4 classes on Mondays.Function: is a rule which assigns an element in
the domain to an element in the range in such a
way that each element in the domain
corresponds to exactly one element in the range.
The notation f(x) read “f of x” or “f at x” means
function of x while the notion y=f(x) means y is a
function of x. The letter x represents the input
value, or independent variable
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This is meant for university students taking either information technology or engineering courses, this course of differentiation, Integration and limits helps you to develop your problem solving skills and other benefits that come along with it.
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The Roman Empire A Historical Colossus.pdfkaushalkr1407
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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.
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Ethnobotany and Ethnopharmacology:
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Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
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The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
3. n=3 n=4 n=5 n=6 n=7 n=8
‘As number of sides of polygon increases, its area
approximates the area of the circle’
‘limit of Area of polygon is the Area of the circle’
As n approaches infinity ,
Lim Area of polygon = Area of the circle
The Idea of
Limits
4. Consider the
function:
The Idea of
Limits 2)( += xxg
2)( += xxg
x
y
O
2
x 1.9 1.99 1.999 1.9999 2 2.0001 2.001 2.01 2.1
g(x) 3.9 3.99 3.999 3.9999 3.0001 4.001 4.01 4.14
4)(lim
2
=
→
xg
x
As x approaches to
positive 2 at both
directions
5. Fundamental Rules of Limits.
1. The Constant Rule
– When we take the limit of a constant, non-
changing function, the limit will simply be that
constant.
1. The Sum Rule
– If two sequences have limits that exist, then the limit of
the sum of sequences is the sum of the limits of the
sequences.
1. The Multiplication Rule
– If two sequences have limits that exist, then the limit of
the product is the product of the limits.
