List MF15 MATHEMATICS (8864) MATHEMATICS (9740) MATHEMATICS (9810) LIST OF FORMULAE AND STATISTICAL TABLES PURE MATHEMATICS Algebraic series Binomial expansion: n n n (a + b) n = a n + a n −1b + a n − 2b 2 + a n − 3b3 + K + b n ‚ where n is a positive 1 2 3 n n! integer and = r r!(n − r )! Maclaurin’s expansion: x2 x n (n) f ′′(0) + K + f (0) + K n! 2! n(n − 1) 2 n(n − 1) K (n − r + 1) r x +K (1 +
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and gaining freedom. When turning this age‚ you are allowed to join the military‚ get married and receive all the rights and responsibilities of an adult. However‚ having a wedding at this age means that during the celebration‚ one is not allowed to share a glass of Champaign during the toasts because the drinking age is 21. The United States is one of the few countries in the world to have such a high legal drinking age. Therefore the drinking age should be lowered to 18 because you are able to
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EFFECT OF ORGANIC AND INORGANIC FERTILIZER ON OKRO CHAPTER ONE (1) 1.1 INTRODUCTION Okra was domesticated in West and Central Africa (Cobley and Steele‚ 1976) and known as ‘Okro’ in the Anglophone African countries as a fast growing common annual vegetable widely consumed in Africa (Schippers‚ 2000). It is one of the numerous vegetable crops cultivated in Nigeria (Anon‚ 1989) where a total of 1 – 2 million hectares
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Legal Drinking Age‚ Why It Should Be Lowered According to Fabian Grund‚ in Why the Legal Drinking Age Should Be Lowered‚ lowering the drinking age comes with many pros‚ including less binge drinking‚ less illegal substance use‚ and if consumed properly‚ it could even be good for your health (Grund 5-8). In the article‚ Fabian Grund says it best: “You can take responsibility to buy a gun‚ get killed in combat or vote for your president‚ but you can’t even buy a damn beer.” (2) In other countries
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words a felony is a big deal. Felons have been convicted of a crime including‚ or in the same category as murder‚ rape‚ arson‚ and burglary. It is because of this that many believe that felons do not deserve the right to vote. Those against felons voting believe that those convicted of crime have shown bad-judgment‚ which proves them unfit to make good decisions‚ especially choosing the nation’s leaders (“ProCon.org”). There are also those however‚ that believe that felons have paid enough of a price
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countries has different definitions. The united States statistically speaking‚ ages from 15-24 years. One thing that is clear is that the terrorist groups today recruit and influence youths to carry out acts that horrifying. Sad to say many youths‚ no matter of race‚ religion‚ educational background or economic status has fallen prey to the rhetoric promoted by these terrorist groups .According to the US Census Bureau‚ lower-class youth commit four times more violent crimes than middle-class youth (2008)
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The 15th of August has its own importance for us Indians. It was on this day in 1947 that India became independent. We won freedom after a hard struggle. On this day our first Prime Minister‚ Pandit Jawaharlal Nehru‚ unfurled the National Flag at the Red Fort for the first time All the people irrespective of their caste‚ colour and creed celebrate the day every year amidst great rejoicing. It is a public holiday. On this day we take a pledge to defend our freedom with all our might. The Independence
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Imagine living in one place all of your life. In this place you have a home‚ a family‚ friends‚ activities that you have committed yourself to and possibly even a car. You feel safe in this place and most likely have developed an everyday rut of doing things. Change doesn’t happen often in this place and if it does the transition of one thing to the next is uneventful. Well‚ this is all about to change. You are now going to be uprooted from your place‚ your home‚ your family‚ your friends and
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Chapter 15 – Mankiw SOLUTIONS TO TEXT PROBLEMS: Quick Quizzes 1. A market might have a monopoly because: (1) a key resource is owned by a single firm; (2) the government gives a single firm the exclusive right to produce some good; or (3) the costs of production make a single producer more efficient than a large number of producers. Examples of monopolies include: (1) the water producer in a small town‚ who owns a key resource‚ the one well in town; (2) a pharmaceutical company that is given a patent
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PROJECT REPORT ON PROJECT REPORT ON ONLINE VOTING SYSTEM SUBMITTED TO Pawan Kumar SUBMITTED BY-Nitin Bhasin Course Core JAVA(CRJV4) ACKNOWLEDGEMENT It is my pleasure to acknowledge you that I have received a project on Online Voting System from my teacher. My first sincere appreciation and gratitude goes to Mr. Pawan Kumar Mahi (Group Leader) for her guidance‚ constructive comments‚ valuable suggestions and inspirations. During
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