Essays on Calculus

Part 1:

1.
This notation means that the limit of a function f(x) as x tends to a is equal to L. In this case, L is a number. a is a number. x is the function. No we cannot conclude anything about f (a).
2.

The three conditions associated with non-existence of a limit are

- Divergence up to infintiy
- Oscillations with a frequency increasing with time
- Scintillation
3.
Limx-a f(x) = ∞means that the limit of the function as x tends to a is infinity while Limx-∞ f(x) = b means that as the limit of the function as x tends to infinity is equal to

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One of the dark secrets of Newton is his deep curiosity and obsession to religion and his devotion to occult. Another revelation shows that Newton has tried to enter pseudoscience which means he settled on beliefs and practices that are mistakenly known as based on scientific method given that before everything, he believes that everything in this world can be subscribed to scientific understanding. According to Walter Lewin, one of the speakers in the video, Isaac Newton is allergic to criticisms even before that is why he decided on keeping his inventions and even the other earthly manners that

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1. Integration is a topic within calculus that has been applied in many engineering problems. Sir Isaac Newton and Gottfried Wilhelm von Leibniz first developed integration concepts, while working independently, in the 15th century (Goldman and Foresta, 2005 p. 4). Leibniz used integral calculus to work on sequences of functions while Newton used it to find the area under a curve and consequently overlook the use of indivisibles (Goldman and Foresta, 2005 p. 5). A separate, but similar in concept discoveries, lay the foundation for the two part fundamental theorem of calculus.
The first part states that, if f

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Validity and Scope of Approximate Methods of Integration

Introduction
Addition of discrete numbers is pretty straightforward; more than 80% of the human population can make mental calculations instantly. So when integration was introduced as a kind of addition in a continuous domain, I was not very worried. However, it didn’t take me long to realize that understanding integration is more than solving a bunch of problems using well defined techniques. So in my pursuit to understand the topic well, I decided to research upon how some of these techniques (Trapezium Rule and Simpson’s Rule) came about, how they work, and what they really mean. With

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Since its creation in the 17th century the mathematics of calculus allows different fields of study the ability for measuring change and motion connected with natural and physical science including medical research and proactive applications of medicine. With the onset of the 21st century, the advances in mathematical insights forming definitions and theorems underpin the variety of uses of calculus in medicine. Calculus provides the abstract mathematical understanding of varieties of professional fields. These include economic trends, biological probabilities with ocean currents, meteorologist calculations of upper atmosphere airflow for weather prediction, and space scientists designing remarkable aircraft for space

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Economics is not Mathematics but mathematics has a great help for economics. It has a dose of reality to some economist according to Michael Edesess, a mathematician. Mathematics from economics has a major difference; there is no mathematician that uses a term in a formula or any statement of any theorem if the said term has defined with accuracy. Economists defined terms such as aggregate demand or economic growth but a thorough study on some real mathematics is suggested to assure an exact definition of the term. Overviews on both subjects are necessary to ensure clarity and depth of

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Calculus is widely used in various professional fields such as in engineering, statistics, physics, economics and architecture. Calculus is also considered as the language that scientists, engineers and economists use due to its capability to model and also control numerous systems. The tasks performer by these professionals usually has a massive impact on people’s lives such as in communication, medicine, electronics, economy, transport and also in national defense.
Calculus is widely applied in the field of engineering in modeling and controlling systems. Electrical engineer often uses integration in determining the precise length of power cables that are required

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The discovery of calculus, which is a branch within mathematics, is attributed to both Isaac Newton and Gottfried Leibniz. Both Isaac Newton and Gottfried Leibniz made independent contributions towards the development of the foundations of calculus. Instrumental and significant contributions were done by both Newton and Leibniz in a bid to ensure that calculus was developed in order to assist in various concepts and applications of mathematics (Kleiner 139). However, it is important to note that the foundations of calculus developed by Newton differed widely from the foundations of calculus that were developed by Leibniz. There is no doubt

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Karl Theodor Wilhelm Weierstrass was a German mathematician who is often called as the "father of modern analysis".

Weierstrass was interested in the soundness of calculus, and also made significant advancements in the field of calculus of variations. Among the several significant axioms, Weierstrass established a necessary condition for the existence of strong extrema of variational problems.
As we know, Cauchy gave a form of the (ε, δ)-definition of limit, in the context of formally defining the derivative, in the 1820s, but did not correctly distinguish between continuity at a point versus uniform continuity on an interval, due to insufficient rigor. Notably, in his 1821 Cours d'analyse, Cauchy gave a famously incorrect proof that the (pointwise) limit of (

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