170 CHAPTER 5. RECURSION AND RECURRENCES 5.2 The Master Theorem Master Theorem In the last section‚ we saw three different kinds of behavior for recurrences of the form aT (n/2) + n if n > 1 d if n = 1. T (n) = These behaviors depended upon whether a < 2‚ a = 2‚ and a > 2. Remember that a was the number of subproblems into which our problem was divided. Dividing by 2 cut our problem size in half each time‚ and the n term said that after we completed our recursive work‚ we had n
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UNIT 2 THEOREMS Structure 2.1 Introduction Objectives PROBABILITY 2.2 Some Elementary Theorems 2.3 General Addition Rule 2.4 Conditional Probability and Independence 2.4.1 Conditional Probability 2.4.2 Independent Events and MultiplicationRule 2.4.3 Theorem of Total Probability and Bayes Theorem 2.5 Summary 2.1 INTRODUCTION You have already learnt about probability axioms and ways to evaluate probability of events in some simple cases. In this unit‚ we discuss ways to evaluate
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pressure dynamics specified by Bernoulli’s Principle to keep their rare wheels on the ground‚ even while zooming off at high speed. It is successfully employed in mechanism like the carburetor and the atomizer. The study focuses on Bernoulli’s Theorem in Fluid Application. A fluid is any substance which when acted upon by a shear force‚ however small‚ cause a continuous or unlimited deformation‚ but at a rate proportional to the applied force. As a matter of fact‚ if a fluid is moving horizontally
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Boyle’s Law 5-1: Boyle’s Law: Pressure and Volume Robert Boyle‚ a philosopher and theologian‚ studied the properties of gases in the 17th century. He noticed that gases behave similarly to springs; when compressed or expanded‚ they tend to ‘spring’ back to their original volume. He published his findings in 1662 in a monograph entitled The Spring of the Air and Its Effects. You will make observations similar to those of Robert Boyle and learn about the relationship between the pressure and volume
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Boyles’ Law Use Boyles’ Law to answer the following questions: 1) 1.00 L of a gas at standard temperature and pressure is compressed to 473 mL. What is the new pressure of the gas? 2) In a thermonuclear device‚ the pressure of 0.050 liters of gas within the bomb casing reaches 4.0 x 106 atm. When the bomb casing is destroyed by the explosion‚ the gas is released into the atmosphere where it reaches a pressure of 1.00 atm. What is the volume of the gas after the explosion
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The Coase Theorem In “The Problem of Social Cost‚” Ronald Coase introduced a different way of thinking about externalities‚ private property rights and government intervention. The student will briefly discuss how the Coase Theorem‚ as it would later become known‚ provides an alternative to government regulation and provision of services and the importance of private property in his theorem. In his book The Economics of Welfare‚ Arthur C. Pigou‚ a British economist‚ asserted that the existence
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Purpose and Method: The purpose of this experiment was to understand Boyle’s Law. In the experiment the pressure in the system under constant temperature and mass was used to confirm if the laws are true. Boyles law relates pressure and volume while all other factors are consistent and states: for a fixed amount of gas kept at constant temp‚ the product of the pressure of the gas and its volume will remain constant if either quantity is changed‚ or where k is constant. The experiment consisted
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Thevenin Theorem It provides a mathematical technique for replacing for a given network‚ as viewed from two output terminals by a single voltage source with a series resistance. It makes the solution of complicated networks (particularly‚ electronic networks) quite quick and easy. The Thevenin’s theorem‚ as applied to d.c. circuits‚ may be stated as under: The current flowing through a load resistance RL connected across any two terminals A and B of a linear‚ active bilateral network is given
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Taylors Theorem: Taylor’s theorem gives an approximation of a n times differentiable function around a given point by a n-th order Taylor-polynomial. For analytic functions the Taylor polynomials at a given point are fixed order truncations of its Taylor’s series‚ which completely determines the function in some locality of the point. There are numerous forms of it applicable in different situations‚ and some of them contain explicit estimates on the approximation error of the function by its Taylor-polynomial
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Thomas Theorem A teacher believing a student is more intelligent than they really are could change the interaction between this student and the teacher in many ways. This student could see the teacher having faith in them and perhaps seeing something in them that they don’t see in themselves. It could cause the student to have higher self esteem by this teacher thinking positively about them. This could be detrimental to the student because other students could consider the extra attention
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