Integral calculus is the study of mathematical integration dealing with integrals. These integrals‚ also known as area under the curve‚ are used to determine the following: areas‚ volumes‚ and lengths. There are a multitude of areas of real-world mathematics to which integral calculus is used. Integration is most often applied in physics‚ biology‚ and even chemistry. Integration is applied to physics in many situations. One important situation is finding the moment of inertia. The moment of inertia
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P8-1 a) Expected Rate of Return $ $ $ Y 55‚000 6‚800 55‚000 X Previous Market Value Cash Flow Current Market Value X 20‚000 $ 1‚500 $ 21‚000 $ Y 12.50% 12.36% X: rt = (Ct + P rt = ($1‚50 rt = 0.125 = b) Both investments are equally risky. Keel should recommend Investment X because it has a Pt - Pt-1) / (Pt-1) Y: rt = (Ct + Pt - Pt-1) / (Pt-1) 0 + $21‚000 - $20‚000) / ($20‚000) rt = ($6‚800 + $55‚000 - $55‚000) / ($55‚00 = 12.5%
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Understand the concepts of derivatives. • Understand linear approximations. • Understand the relationship between integration and differentiation and continuity. Learning Outcomes: After completing this unit‚ students will be able to: 1. describe the basic ideas concerning functions‚ their graphs‚ and ways of transforming and combining them; 2. use the concepts of derivatives to solve problems involving rates of change and approximation of functions; 3. apply the differential calculus to solve optimization
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d dʒ g/ (+ nasals /m n ŋ/) → trills and taps (dental/alveolar [ɾ]‚ [r]‚ uvular [R]) Close approximation‚ producing friction → fricatives /f θ s ʃ h v ð z ʒ/ → [x ʍ] Scottish English Open approximation (no/weak obstruction of air-flow) → approximants /w j r l/ Important “sub-categories” / alternative categorisations: Oral closure with free nasal passage → nasals ( or nasal “stops”) /m n ŋ/ Open approximation with free airflow along side(s) of tongue → lateral (approximant) /l/ Approximants and nasals
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so large‚ that a purely analytical solution to the equations is not tractable. It is in these complex systems where computer simulations and numerical methods are useful. The techniques for solving differential equations based on numerical approximations were developed before programmable computers existed. During World War II‚ it was common to find rooms of people (usually women) working on mechanical calculators to numerically solve systems of differential equations for military calculations
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My purpose in writing this is to argue for the existence of an objective morality based entirely on rational and scientific reasoning. By "objective morality" I do not simply mean that morality exists in the sense that various societies consider various actions to be immoral. What I mean is that certain actions are inherently right or wrong regardless of what any society thinks about them. In other words‚ I mean that there is an "objective morality" which exists independently of human beliefs and
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Calculus is the mathematical study of change‚[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches‚ differential calculus (concerning rates of change and slopes of curves)‚ and integralcalculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental
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3. Differences between APV and option valuation Valuing MW Acquisition by using APV method assumes in practice that exploiting of all MW’s reserves is certain and happens right after the acquisition. In other words‚ the APV method excludes the flexibility in future decision making. In this case‚ Apache has both an option to defer the exploiting of reserves into future and Apache may also choose not to exploit the MW reserves at all. As some of MW’s reserves are actually real options‚ the APV valuation
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John Doe Fin 4980-01 Dr. Alex 2/18/2013 Project 1: “Foundations of Portfolio Theory” by. H.M. Markowitz (1991) Foundations of Portfolio Theory by H.M. Markowitz is based on a two part lesson of microeconomics of capital markets. Part one being that taught by Markowitz‚ which is solely geared toward portfolio theory and how an optimizing investor would behave‚ whereas part two focuses on the Capital Asset Pricing Model (CAPM) which is the work done by Sharpe and Lintner. In this article Markowitz
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1. Finding An Initial Basic Feasible Solution: An initial basic feasible solution to a transportation problem can be found by any one of the three following methods: I. North West Corner Rule II. The Least Cost Method III. Vogel’s Approximation Method 1. North West Corner Rule The North West corner rule is a method for computing a basic feasible solution of a transportation problem‚ where the basic variables are selected from the North-West Corner (i.e. top left corner).
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