Leibniz and Calculus Calculus is the field of mathematics that analyses aspects of change in processes or systems that can be modelled by functions. ... Calculus dates back to the ancient Greeks. ... There is the "Power Rule- which states: if f(x) = xⁿ, where n is any real number, then f'(x)=nxⁿ. Secondly, there is the Sum and difference Rule which states: if h(x) = f(x) +/- g(x), then h'(x) = f'(x) +/- g'(x). ... Finally, there is the "Chain Rule- which states: if h(x) = f(g(x)), then h'(x) = (g(x)) • g'(x). ...

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For example, the term function can be used to designate a power xn of a variable x. ... Dirichlet regarded y = x2 - 3x + 5 as a function which is thought of as the rule that determines y for a given x of an ordered pair of the function; thus, the preceding rule determines (3, 5), (-4, 33) as two of the infinite number of elements of the function. ... Another type of limit important in the study of calculus can be illustrated as follows. ... Mathematical induction can be uses as a way of proving that certain rules are true for all positive integers; Axiom of Induction: where S is a subset of po...

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Invention of Calculus was one of the greatest discoveries ever. ... Newton was the first to apply calculus to general physics and Leibniz developed much of the notation used in calculus today; he often spent days determining appropriate symbols for concepts. ... Today, both Newton and Leibniz are given credit for developing calculus independently. ... Newton called his calculus "the science of fluxions". ... The best known of today' calculus was published by Newton. ...

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During many Calculus courses the Concept of Limits are taught to students by showing them how, but not why. ... Now Limits have certain rules to follow if they want to be Limits. ... Since, we already know about the rule of left and right hand limits so we"re one third of the way there. ... This is used when your dividing expressions with variables such as x^3 or x to the third power. ... Limits are an integral part of calculus. ...

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Another early calculating tool was called the "Slide Rule". ... The slide rule made multiplication and division much easier. Engineers and scientists used the slide rules until the invention of calculator in the early 1970's. ... Some have the ability to do complicated geometric, algebraic, trigonometric, statistical, and calculus functions. Now calculators operate on electrical power either by batteries, or solar cells. ...

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He was also known for his invention of the differential and integral calculus. ... Now what about your Calculus you supposedly invented? ... GL: I developed differential and integral Calculus. I introduced the integral notation and developed the product and quotient rules for differentiation. I also discovered the power rule for both integral and fractional n. ...

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The Geneva Conventions rules only apply to "prisoners of war.... The merits of torture must be looked at using utilitarian calculus or cost-benefit analysis. ... If cost-benefit analysis and utilitarian calculus is so pervasive that it is even drawn from our psychological biology, and can be found in the very confines of the wild, this of course then shirks the argument that aggression in the form of "torture" can be considered "inhumane.... Some claim that it is an unspoken rule that is understood in human nature – that if you run with a certain crowd, you are aware ...

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The Geneva Conventions rules only apply to "prisoners of war.... The merits of torture must be looked at using utilitarian calculus or cost-benefit analysis. ... If cost-benefit analysis and utilitarian calculus is so pervasive that it is even drawn from our psychological biology, and can be found in the very confines of the wild, this of course then shirks the argument that aggression in the form of "torture" can be considered "inhumane.... Some claim that it is an unspoken rule that is understood in human nature – that if you run with a certain crowd, you are aware ...

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JEREMY BENTHAM • Founder of Utilitarian School, which proposed that people maximize pleasure and minimize pain (felicific calculus), and that these impulses were the source of human motivation. ... NICCOLO MACHIAVELLI • Utopia • The Prince 1513; lesson on expediency; how an individual can take power and hold on to it. ARISTOTLE • "many head are better than one" • but the best form of government is not democracy, but rule by the many in the interest of all. • Anticipates the kind of popular self-rule that came to be called "republican. ... • T...

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In the abiding shadow of total war, and in the midst of a global hypertechnological economy, the inexorable dictates of interdependence have radically redefined mainstream power. ... The indictment of sitting heads of state, such as Slobodan Milosevic, became a defining moment for the rule of law in its most stark sense, embodying the proposition-captured in the Nuremberg Judgment's aphorism-that "[c]rimes against international law are committed by men, not by abstract entities, and only by punishing individuals who commit such crimes can the provisions of international law be enforced."2...

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Candide, which reflects Voltaire's life-long hatred of Christian regimes of power and the arrogance of nobility, is a prime example of the philosophical values of the Enlightenment. ... For example L'Hospital's a French Noble, had in his "possession- mathematicians that developed new ways of taking limits (a Calculus idea). Yet in today's society we call this way "L'Hospital's Rule,"" not Bernoulli's rule who is the one who "invented- it. ... He did not trust the power of reason to help conquer contemporary social conditions. ...

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He couldn't actively play any games with the other kids; therefore, he would amuse himself by building mechanical toys like wooden clocks, sundials, and mouse powered flour mills. ... Newton's god made the rules to how the universe operates. ... Newton was really upset because like I stated before, god makes the rules how the universe operates, and Descartes proposal not only was wrong but went against god. ... He accomplished the following: developed calculus, laid the foundations of his theory of light and color and studied planetary motion. ... Newton was the first to develop...

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He described the principles of utilitarianism with the phrase, "calculus of happiness," which explains whether actions are deemed either good or bad, while considering many variables such as duration, likelihood, and intensity (Mautner). ... Providing a moral thought process for the average person or individual holding a power in office, which will lead to the best decision being made from a utilitarian point of view. ... Utilitarianism provides the solution with the greatest utility, but often tied to great moral difficulty, while the theory of natural rights provides a set of mora...

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We propose a discussion on preliminary results of a literature review pilot study regarding the use of CAS in post-secondary education. Several issues surrounding technology integration emerged from our review, and these are described in detail within the paper. The brief report on the type of analy...

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The Church held its power throughout the Renaissance but with great power comes great responsibility and some fell victim to greed. "The Pope, who had the responsibility of running the Catholic Church as well, ruled Rome. As the power of the northern city-states grew, the Papacy increasingly became the seat of an international politician rather than a spiritual leader, and many pontiffs fell prey to the vices of corruption and nepotism that often accompanied a position of such power."... The invention of the printing press technology brought about a great power to the people. ...

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Never before had a European monarch even set foot in a New World colony let alone settle in one as the focus of power. ... Enlightened despotism is an absolute monarch which uses the power of the crown to impose the most up to date administrative mechanisms and technology on the country for the welfare of everyone. ... They were aided by a newly developed type of mathematics which no one likes, calculus, and with this the Enlightenment scientists were opening a whole new understanding of the physical world. ... One such case of this is a thinly disguised attack on the governor's rule thro...

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The French had expanded their rule and hoped to expel the English. ... He saw the Prince Borgia as the only hope for revitalizing the spirit of independence among his temporaries making them fit for republican rule Erasmus- expert in handling greek and latin. ... He wanted to enhance centralized royal power and xpand French influence in the larger theater of Europe. ... He processed power and became exasperated by the attempts of the legislators to perpetrate themselves to office and to profit by confiscating the wealth of their opponents. ... The revolution consolidated the position of larg...

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Odo Nobunga decreased the power of the Buddha, placed the shogunate under his power, and was seen more as a tyrant than a leader. ... Once Tokugawa came to power, he immediately went into action and confiscated much of the land of Japan, then redistributed a majority of it to himself and his men, which gave them the central control needed to maintain influence throughout all of Japan. ... In fact Louis often preached, "I am the state," which was similar to Tokugawa's rule. ... Japan was overall a peaceful country, but many leaders feared that outsiders would come in and corrupt their orde...

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For me, Mathematics is the creation of order from chaos, the application of rules to the anarchic world in which we live in order to achieve a definitive solution, which is both simple and elegant but also guaranteed to be correct assuming that the procedure being used has been followed without error. ... For example, when studying Vector Calculus the ability to visualise the particular shape whose surface integral one is required to find is very useful when one is not actually given the shape in question, only the defining equation. However, as Charles Darwin states in The Descent of Ma...

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The author talks about how life in the dormitories has radically changes her views on rules and morality of Yale College. ... Hacks main argument seems to be the rules that Yale has implemented on their freshman and sophomore class requiring them to live on campus in college dormitories. ...

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The Dream Yet to be Realized. Almost fifty years have passed since the U.S. Supreme Court declared, in Brown v. Board of Education of Topeka, Kansas, that laws separating the races in school are unconstitutional. Hundreds of lawsuits later, black and white students were bused back and for...

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Our only rule is to stay within the fence. ... Teams are clubs; victories and defeats are real, not made-up; and rules are presumably applied evenly. ... Many sports psychologists and physical educators believe that before age 12, children simply aren't ready to perform the complex sequences of skills that many team sports require, just as calculus would flummox a kid still struggling with long division. ...

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I am going to take you through a journey on the back of a traveller that is old and weary. You will recognise the traveller and will know a lot about it. The traveller is on a journey, it has been to the past, is in the present and headed for the future and our traveller is asking questions of the...

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Krannawitter points out, the "Southern demand for federal slave protection represented a demand for an unprecedented expansion of federal power." ... Buchanan said that the Dred Scott decision was proof that the South had no reason for secession, and that the Union "... was intended to be perpetual," but that, "The power by force of arms to compel a State to remain in the Union," was not among the "... enumerated powers granted to Congress." the National Banking Act and the authorization of United States Notes by the Legal Tender Act of 1862. ...

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