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Acknowledgement First of all, I would like to say thank you to my parents for providing everything,such as money, to buy anything that are related to this project work,their advise, whichis the most needed for this project and facilities such as internet, books, computers andall that. They also supported me and encouraged me to complete this task so that I willnot procrastinate in doing it. Then I would like to thank to my teacher, Pn Lui for guiding me throughout thisproject. Even I had some di

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AcknowledgementFirst of all, I would like to say thank you to my parents forproviding everything,such as money, to buy anything that are relatedto this project work,their advise, whichis the most needed for thisproject and facilities such as internet, books, computers andall that. They also supported me and encouraged me to complete this task sothat I willnot procrastinate in doing it. Then I would like to thank to my teacher, Pn Lui for guiding methroughout thisproject. Even I had some difficulties in doing this task,but she taught me patiently untilwe knew what to do. She tried andtried to teach me until I understand what I¶msupposed to do with theproject work.Besides that, my friends who always supporting me. Even thisproject isindividually but we are cooperated doing this projectespecially in disscussion andsharing ideas to ensure our task will finishcompletely.Last but not least, any party which involved either directly or indirect incompleting this project work. Thank you everyonINTRODUCTIONCalculus is a branch in mathematics focused on limits, functions,derivatives, integrals, and infiniteseries.This subject constitutes a majorpart of modern mathematics education. It has two majorbranches,differential calculus and integral calculus, which are related by thefundamental theoremof calculus. Calculus is the study of change, in thesame way that geometry is the study of shapeand algebra is the studyof operations and their application to solving equations. A courseincalculus is a gateway to other, more advanced courses inmathematics devoted to the study offunctions and limits, broadly calledmathematical analysis. Calculus has widespread applications inscience,economics, and engineering and can solve many problems for whichalgebra alone isinsufficient.Historically, calculus was called the calculusof infinitesimals , or infinitesimalcalculus . More generally, calculus
may refer to any method or system of calculation guided by thesymbolicmanipulation of expressions. Some examples of other well-known calculiarepropositional calculus, variational calculus, lambda calculus, picalculus, and join calculus.History The product rule and chain rule, the notion of higher derivatives, Taylorseries, and analyticalfunctions were introduced by Isaac Newton in anidiosyncratic notation which he used to solveproblems of mathematicalphysics. In his publications, Newton rephrased his ideas to suitthemathematical idiom of the time, replacing calculations withinfinitesimals by equivalentgeometrical arguments which wereconsidered beyond reproach. He used the methods ofcalculus to solvethe problem of planetary motion, the shape of the surface of a rotatingfluid, theoblateness of the earth, the motion of a weight sliding on acycloid, and many other problemsdiscussed in his PrincipiaMathematica. In other work, he developed series expansionsforfunctions, including fractional and irrational powers, and it was clearthat he understood theprinciples of the Taylor series.These ideas weresystematized into a true calculus of infinitesimalsby Gottfried WilhelmLeibniz, who was originally accused of plagiarism by Newton. He isnowregarded as an independent inventor of and contributor to calculus.His contribution was to providea clear set of rules for manipulatinginfinitesimal quantities, allowing the computation of secondand higherderivatives, and providing the product rule and chain rule, in theirdifferential andintegral forms. Unlike Newton, Leibniz paid a lot of attention to the formalism ± he often spentdays determiningappropriate symbols for concepts. Leibniz and Newton are usually bothcreditedwith the invention of calculus. Newton was the first to applycalculus to general physics andLeibniz developed much of the notationused in calculus today. The basic insights that bothNewton and Leibnizprovided were the laws of differentiation and integration, second andhigherderivatives, and the notion of an approximating polynomial series. ByNewton's time, thefundamental theorem of calculus was known

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