Calculus I Midterm 2 November 2013 2 1. (6 marks) Find the following limit: lim (1 + sin 7 x ) cot 5 x x →0 + ( 2. (3 marks) Find the derivative of y = 3 x + 5 2 ) sec x Calculus I Midterm 2 November 2013 3 3. (Total 8 marks) Answer each question in the space provided. Do NOT simplify your answer. x2 − x 3 dy of the function f ( x) = ln( x3 ) a) Find dx e [ ( )] b) If f ( x) = arcsin x c) Find ( ( d sin 2 dx d) If f ( x)
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and integration) was developed to improve this understanding. Differentiation and integration can help us solve many types of real-world problems. 1. We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost‚ strength‚ amount of material used in a building‚ profit‚ loss‚ etc.). 2. Derivatives are met in many engineering and science problems‚ especially when modelling the behaviour of moving objects. 3. Calculus is also a base of economics. 4. It is
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disciplines.Differential equations arise in many areas of science and technology: whenever adeterministicrelationship involving some continuously varying quantities (modelled byfunctions) and their rates of change in space and/or time (expressed as derivatives) isknown or postulated. This is illustrated inclassical mechanics‚ where the motion of a body is described by its position and velocity as the time varies.Newton’s Lawsallowone to relate the position‚ velocity‚ acceleration and various forces acting
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TPG4160 Reservoir Simulation 2012 Lecture note 1 page 1 of 11 INTRODUCTION TO RESERVOIR SIMULATION Analytical and numerical solutions of simple one-dimensional‚ one-phase flow equations As an introduction to reservoir simulation‚ we will review the simplest one-dimensional flow equations for horizontal flow of one fluid‚ and look at analytical and numerical solutions of pressure as function of position and time. These equations are derived using the continuity equation‚ Darcy’s equation
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Syndicate 2 1. Describe the key factors‚ strategies that led to and the lessons learned from the demise of Long Term capital Management. Provide a brief summary of what happened and what were the strategies used by the fund. The most well know strategy which hedge fund managers or practitioners undertake was “market neutral arbitrage”‚ thus‚ from this particular trading strategy‚ of course what they are doing is not like what the name suggested “hedging”‚ instead‚ hedge fund participants
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Calculus provides the language of economics and the means by which economists solve problems. Calculus is especially significant in illustrating what a leading economist calls a key principle of economics. Calculus focuses heavily on functions and derivatives. In economic research they often examine functional relationships for example relationship between the dependent variable income and various predictors‚ or independent variables‚ such as education and experience. Its benefit in economics is that
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Written Report Case: The Collapse of Barings Derivatives & Risk Control The Collapse of Barings: The Events and The Aftermath Group Write-up Written Report Case: The Collapse of Barings Executive Summary Barings Bank after two centuries of successful operations became a victim of a rogue trader. US$1.3 billion in losses outweighed bank’s own capital of US$850 million. Management negligence‚ lack of internal controls‚ poor risk management and excessive risk-taking strategy brought the bank
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Differential Equations Second Order Differential Equations Introduction In the previous chapter we looked at first order differential equations. In this chapter we will move on to second order differential equations. Just as we did in the last chapter we will look at some special cases of second order differential equations that we can solve. Unlike the previous chapter however‚ we are going to have to be even more restrictive as to the kinds of differential equations that we’ll look at
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Lam Tran BBUS 435 – Accounting Information System Rogue Trader COSO Control Violations Short Essay The movie‚ Rogue Trader‚ narrates the true story of a man named Nick Leeson. He brought the Barings Bank down‚ which was one of the most venerable financial institutions in England. Nick Leeson was played by the actor Ewan McGregor‚ who started working in Indonesia for Barings Bank. He then became a trader on the floor of Singapore International Monetary Exchange. Nick’s responsibility was to trade
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Without knowing something about differential equations and methods of solving them‚ it is difficult to appreciate the history of this important branch of mathematics. Further‚ the development of differential equations is intimately interwoven with the general development of mathematics and cannot be separated from it. Nevertheless‚ to provide some historical perspective‚ we indicate here some of the major trends in the history of the subject‚ and identify the most prominent early contributors. Other
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