Chap-04 B.V.Ramana August 30‚ 2006 10:13 Chapter 4 Calculus of Variations function of the independent variable y(x)‚ which is a function. Thus L{y(x)} = Y cn c2 A O c1 X B x2 x1 4.1 INTRODUCTION Calculus of variations deals with certain kinds of “external problems” in which expressions involving integrals are optimized (maximized or minimized). Euler and Lagrange in the 18th century laid the foundations‚ with the classical problems of determining a closed curve in the plane
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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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Tuple Relational Calculus ( TRC ) Introduction Procedural Query language query specification involves giving a step by step process of obtaining the query result e.g.‚ relational algebra usage calls for detailed knowledge of the operators involved difficult for the use of non-experts Declarative Query language query specification involves giving the logical conditions the results are required to satisfy easy for the use of non-experts Prof P Sreenivasa Kumar‚ Department of CS&E‚ IITM. 1 TRC
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Free Response Questions 1969-2005 Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom 1 AP Calculus Free-Response Questions 1969 AB 1 Consider the following functions defined for all x: f1 ( x) = x f 2 ( x) = x cos x f3 ( x) = 3e2 x f 4 ( x) = x − x Answer the following questions (a‚ b‚ c‚ and d) about each of these functions. Indicate your answer by writing either yes or no in the appropriate space in the given rectangular grid. No justification
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Find the x coordinates of all relative extreme points of[pic]. |A)[pic] |B) [pic] |C) [pic] |D) [pic] |E) [pic] | [pic] First find the derivative of the function[pic]‚ f ’(x): |[pic] |= |[pic] |apply power rule
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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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the river to the tanks. To minimize the cost of the pipeline‚ how far from the refinery should P be located? (Round your answer to two decimal places.) 1 year ago Report Abuse Colorado... Best Answer - Chosen by Voters This is a min-max calculus problem‚ where we want to minimize the cost function: We need a drawing of the situation: see https://docs.google.com/drawings/d/1PvkU… where R is the refinery‚ O will be the x-axis origin‚ P is the point on the north bank‚ and x= distance
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Integration in the Medical Field Calculus is a very versatile and valuable tool. It is a form of mathematics‚ which was developed from algebra and geometry. It is made up of two interconnected topics‚ differential calculus and integral calculus. Last week‚ my teacher was talking about the benefits of using Integration in daily life. She encouraged us to think about what we will do in our profession and to find examples of the application of calculus concepts. It made me wonder if there is
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Maxima and Minima First Derivative Test 1) We are given the function First‚ we find the derivative: We set the derivative equal to 0 and solve: Since the domain of f is the same as the domain of f’‚ 4 is the only critical number of f. Testing: x < 4 | f’(0) = -8 | f is decreasing | x > 4 | f’(5) = 2 | f is increasing | By the First Derivative Test‚ x = 4 is a local minimum. 2) We are given the function First‚ we find the derivative: We set the derivative
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X 410 “Business Applications of Calculus” PROBLEM SET 1 [100 points] PART I As manager of a particular product line‚ you have data available for the past 11 sales periods. This data associates your product line’s units sold “x” and total PROFIT “P” results for these sales periods. Product Red03 Units [x] Profit [P] 10 20 100 130 190 240 300 320 380 430 500 -33986 -31792 -9200 790 21418 37728 54000 58208 65840 65050 50000 1 Section A: 1st Order Model
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