...The Application of the Profit Function in a Business’s Growth Differential Calculus May 24, 2014 The application of calculus in a business is extremely important since calculus is considered as the study of changes. Its complexity in the study of changes has become one of the humankind’s greatest tool for analyzing changes in the marketplace. The profit function was created with the main purpose for businesses to understand how the changes in revenues and in costs would generate a profit or not profit at all. A profit can be generated when the amount of revenues is higher than the amount of costs. When a business starts, is normal to not gain any profit at all, in fact, most of the time, a business tends to lose money in its first year. However with that information, a business can analyze the money loss of that year and determine any gaps or holes that prevents the maximization of the profit and have a more prosperous result for the following year. For instance, if a company suffer a loss in profit, they can analyze the profit function to determine the main reason of why there was not a positive profit. If they see that the problem of the profit function was a low revenue then they can regulate the sale of products or services and price control, or if the problem lies in the cost function, they can adjust or lower the costs and expenses made by the business. The graph of a profit function can show at what time of the year the company tends to...
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...Calculus From Wikipedia, the free encyclopedia This article is about the branch of mathematics. For other uses, see Calculus (disambiguation). Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem [show]Differential calculus [show]Integral calculus [show]Vector calculus [show]Multivariable calculus Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits,functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modernmathematics education. It has two major branches,differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the 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. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science,economics, and engineering and can solve many problems for which algebra alone is insufficient. Historically, calculus was called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus...
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...MATH 1205 | CALCULUS | 3 | A- | ECON 2005 | MICRO PRINCIPLES OF ECONOMICS | 3 | A- | ACIS 1504 | INTRODUCTION TO BUSINESS INFORMATION SYSTEMS | 3 | B+ | ENGE 1114 | EXPLORATION OF ENGINEERING DESIGN | 2 | A | MATH 1206 | CALCULUS | 3 | B+ | PHYS 2305 | FOUNDATIONS OF PHYSICS | 4 | A | AOE 2074 | COMPUTATIONAL METHODS | 3 | B+ | ECON 2006 | MACRO PRINCIPLES OF ECONOMICS | 3 | A- | ECON 3104 | MICRO ECONOMICS THEORY | 3 | B+ | AOE 2104 | INTRODUCTION TO AEROSPACE ENGINEERING | 3 | A- | ESM 2104 | STATICS | 3 | B | MATH 2224 | MULTIVARIABLE CALCULUS | 3 | A- | AOE 3094 | MATERIALS FOR AEROSPACE AND OCEAN ENGINEERING | 3 | B+ | ACIS 2115 | PRINCIPLES OF ACCOUNTING | 3 | A | BIT 2405 | QUANTITATIVE METHODS | 3 | A | AOE 3104 | AIRCRAFT PERFORMANCE | 3 | B+ | ESM 2204 | MECHANICS OF DEFORMABLE BODIES | 3 | B+ | ESM 2304 | DYNAMICS | 3 | A- | ECON 3204 | MACRO ECONOMICS THEORY | 3 | B+ | MGT 3304 | MANAGEMENT THEORY AND LEADERSHIP PRACTICE | 3 | A | AOE 3054 | AEROSPACE EXPERIMENTAL METHODS | 3 | B+ | AOE 3114 | COMPRESSIBLE AERODYNAMICS | 3 | B | AOE 3124 | AEROSPACE STRUCTURES | 3 | A- | AOE 3134 | STABILITY AND CONTROL | 3 | A | MKT 3104 | MARKETING MANAGEMENT | 3 | B+ | FIN 3104 | INTRODUCTION TO FINANCE | 3 | A | AOE 3044 | BOUNDARY LAYER THEORY | 3 | B | AOE 4154 | AEROSPACE ENGINEERING LAB | 1 | A | AOE 4234 | AEROSPACE PROPULSION | 3 | B | AOE 4266 | DESIGN | 3 | A | FIN 3055 | LEGAL ENVIRONMENT OF BUSINESS | 3 | A- | ...
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...Project Gutenberg EBook of Calculus Made Easy, by Silvanus Thompson This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: Calculus Made Easy Being a very-simplest introduction to those beautiful methods which are generally called by the terrifying names of the Differentia Author: Silvanus Thompson Release Date: October 9, 2012 [EBook #33283] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK CALCULUS MADE EASY *** Produced by Andrew D. Hwang, Brenda Lewis and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive/American Libraries.) transcriber’s note Minor presentational changes, and minor typographical and numerical corrections, have been made without comment. All A textual changes are detailed in the L TEX source file. This PDF file is optimized for screen viewing, but may easily be A recompiled for printing. Please see the preamble of the L TEX source file for instructions. CALCULUS MADE EASY MACMILLAN AND CO., Limited LONDON : BOMBAY : CALCUTTA MELBOURNE THE MACMILLAN COMPANY NEW YORK : BOSTON : CHICAGO DALLAS : SAN FRANCISCO THE MACMILLAN CO. OF CANADA, Ltd. TORONTO CALCULUS MADE EASY: BEING A VERY-SIMPLEST...
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...There are many reasons why I want to take AB Calculus next year. The first reason why I would like to take AB Calculus is that this course will challenge me and help me excel in college when I take other calculus classes. In college, I will be pursuing a major/degree in business, and AB Calculus will lay a solid math foundation for me to excel in college. I will prepare over summer break, with a tutor if necessary, to get caught up with the Honors Pre-Calculus class and make sure that I am ready for AB Calculus when school starts. I missed getting into AP Calculus by one point and I do not want to be in a slow-paced math class my senior year because of this one point. I do not believe that one point should dictate what class I should be placed...
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... Calculus From Wikipedia, the free encyclopedia Jump to: navigation, search This article is about the branch of mathematics. For other uses, see Calculus (disambiguation). | It has been suggested that Infinitesimal calculus be merged into this article or section. (Discuss) Proposed since May 2011. | Topics in Calculus | Fundamental theorem Limits of functions Continuity Mean value theorem [show]Differential calculus | Derivative Change of variables Implicit differentiation Taylor's theorem Related rates Rules and identities:Power rule, Product rule, Quotient rule, Chain rule | [show]Integral calculus | IntegralLists of integrals Improper integrals Integration by: parts, disks, cylindrical shells, substitution, trigonometric substitution, partial fractions, changing order | [show]Vector calculus | Gradient Divergence Curl Laplacian Gradient theorem Green's theorem Stokes' theorem Divergence theorem | [show]Multivariable calculus | Matrix calculus Partial derivative Multiple integral Line integral Surface integral Volume integral Jacobian | | Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the...
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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 integral calculus (concerning accumulation of quantities and the areas under and between curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally considered to have been founded in the 17th century by Isaac Newton and Gottfried Leibniz, today calculus has widespread uses in science, engineering and economics and can solve many problems that algebra alone cannot. Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". The word "calculus" comes from Latin (calculus) and refers to a small stone used for counting. More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, calculus of variations, lambda calculus, and...
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...organized thought. Apart from my major courses, I have been crazy about attending lectures of Economy Department in my college. The effect of market and economy attracted me a lot. Therefore, I completed macroeconomics, microeconomics and accounting in my sophomore year. In addition, my father is taking managing position in an entrepreneur. Accordingly, I have been interested in business courses and I decide to take financial related courses, especially Actuarial Studies as the direction of my master’s study. I have been interested in numbers since I was a high school student. I felt satisfied even though I had to contribute more than one hour to solve a mathematic problem. I often spent time to think about other methods to solve mathematic problems that my teacher had provided answers. My enthusiasm about mathematics was inspired again when I began my college study. I took some basic mathematics concepts, such as limit, series, calculus and differential coefficient. I also learned some basic theories and the application of related concepts, such as differential coefficient of function of one variable, calculus, partial derivative of function of many variables, differential equation, and Taylor's formula, intermediate value theorem and infinite series which help me to know the nature of function, and the independent vector algebra and space analytic geometry. To be honest, I even made more efforts in the study of mathematics than that in my academic courses. Therefore, I believe that...
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...As for what I have been informed, Differential Calculus is simply essential in business. It is best recognized by it’s sub-topic, “the obtainment of derivatives”, which basically represents the average change of income of a business. It is something that simply makes the process of calculations on a business much simpler. Knowing more about it makes me think of the thousands of companies that might be using it without knowing its importance more deeply. Differential Calculus’ applications in business are very extensive. It can be so useful that its applications are seem from calculating the cost of public transport to the costs of making a building. The certain amount of things that need to be used for x thing its also well-defined. If it wouldn’t be by this subject there would certainly be an imbalance in most of the calculation methods used in business. As explained before, one of the commonest but most important topics of this subject is the derivatives, which is the topic I chose to explained in detailed and contrast it with the business area as it’s the one I liked the most. The derivatives are a very useful tool when we related to business, since they have the power to make marginal calculations, in other words it finds the rate of change that’s add up when additional total unit, regardless of the monetary amount being considered: cost, income, profit or production. The derivatives are a very useful tool, since by their very nature they allow marginal calculations...
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...Derivative=limf(x+change in x) –f(x) R=x*p P=R-C Change in x Limits: Point Slope form: y-y,=m(x-x,) Hole (removable discontinuity) Jump: Limit does not exist Vertical Asymptote: Limit does not exist Walking on graph at x=#, what is the y-value? Find the equation of a tangent line on f(x)=1/x at (1,1) Ex1: lim x^2+4x+3 = (-1)^2 +4(-1) +3 =0 point: (1,1) f(x)=x^-1 m=-1 = -1 = -1 = m x-1 x+1 -1+1 0 m=f’(x) f’(x)=-1x^-2 (1)^2 1 ------------------------------------------------- y-1=-1(x-1) y-1=-x+1 = y=-x+2= EQUATION Product Rule: f’(x)=u’v+v’u Quotient Rule: f(x)=h(x)g’(x)-g(x)h’(x)=lowd’high-highd’low [h(x)]^2 bottom^2 Chain Rule: derivative of the outside(leave inside alone)*derivative of the inside Implicit Differentiation: (1) take derivative of each term normally, if term has y on it, we will multiply it by y’ Critical Points: (1) Find f’(x); (2) Set f’(x)=0, solve it; (3) Plot points on # line; (4) Test points around the points in step 3, by plugging them into derivative. If positive: up If negative: down; (5) Write our answer as an interval Max and Mins (relative extrema): (1) Do all the up and down stuff from 3.1; (2) If you went up then down you have a max; if you went down then up you have a min; (3) Label the points (x,y) for max and mins to get the y, go back to f(x) Ex2: f(x) =1/4x^4-2x^2 a) Find the open intervals on which the function is increasing or...
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...University of Connecticut Department of Mathematics Math 1131 Sample Exam 1 Spring 2014 Name: This sample exam is just a guide to prepare for the actual exam. Questions on the actual exam may or may not be of the same type, nature, or even points. Don’t prepare only by taking this sample exam. You also need to review your class notes, homework and quizzes on WebAssign, quizzes in discussion section, and worksheets. The exam will cover up through section 3.2 (product and quotient rule). Read This First! • Please read each question carefully. Other than the question of true/false items, show all work clearly in the space provided. In order to receive full credit on a problem, solution methods must be complete, logical and understandable. • Answers must be clearly labeled in the spaces provided after each question. Please cross out or fully erase any work that you do not want graded. The point value of each question is indicated after its statement. No books or other references are permitted. • Give any numerical answers in exact form, not as approximations. For example, one-third 1 is 3 , not .33 or .33333. And one-half of π is 1 π, not 1.57 or 1.57079. 2 • Turn smart phones, cell phones, and other electronic devices off (not just in sleep mode) and store them away. • Calculators are allowed but you must show all your work in order to receive credit on the problem. • If you finish early then you can hand in your exam early. Grading - For Administrative Use Only Question:...
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...Differentiation Rules (Differential Calculus) 1. Notation The derivative of a function f with respect to one independent variable (usually x or t) is a function that will be denoted by D f . Note that f (x) and (D f )(x) are the values of these functions at x. 2. Alternate Notations for (D f )(x) f (x) d For functions f in one variable, x, alternate notations are: Dx f (x), dx f (x), d dx , d f (x), f (x), f (1) (x). The dx “(x)” part might be dropped although technically this changes the meaning: f is the name of a function, dy whereas f (x) is the value of it at x. If y = f (x), then Dx y, dx , y , etc. can be used. If the variable t represents time then Dt f can be written f˙. The differential, “d f ”, and the change in f , “∆ f ”, are related to the derivative but have special meanings and are never used to indicate ordinary differentiation. dy Historical note: Newton used y, while Leibniz used dx . About a century later Lagrange introduced y and ˙ Arbogast introduced the operator notation D. 3. Domains The domain of D f is always a subset of the domain of f . The conventional domain of f , if f (x) is given by an algebraic expression, is all values of x for which the expression is defined and results in a real number. If f has the conventional domain, then D f usually, but not always, has conventional domain. Exceptions are noted below. 4. Operating Principle Many functions are formed by successively combining simple functions, using constructions such as sum...
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...Computer Assignment Use Wolfram Alpha or any other technology to answer the questions below. Copy all relevant answers into this Word document. Save the Word document and send it to me via email attachment. Do NOT forget to type your name into the document, and include in your responses the commands you used to get the answers. 1. Consider the function f(x)=(e^2x-1)/x Find the limit of f(x) as x approaches zero. 2. Define the function Find the derivative of that function. Find f’(0.67) (the first derivative at 0.67). What does that mean for the function f at the point? Find f’’(0.67) (the second derivative at 0.67). What does it mean for the function f at that point? Find all points where the derivative is zero. A) B) C) D) 3. Define the function Find the derivative of the function and use Wolfram Alpha to confirm your answer. Find all points where the derivative is zero and classify them as local extrema, if possible Determine if f is increasing (going up) or decreasing (going down) between the points found in (b) A) B) Local extreme’s are listed C) Increasing 4. Find the following integrals: a) b) 5. Find the area between the graph of f(x) = (x2 – 4) (x2 - 1) and the x axis. Note that one simple definite integral won’t do it, you will need to carefully determine where the function is positive and negative and integrate accordingly, perhaps using multiple steps. 6. Solve the system...
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...Gateway Case Analysis As part of our analysis, we focused on the following goals: 1) Minimize the chance of aircraft crash losses and insurance costs combined exceeding $37 million in the next year, and 2) Obtain the insurance coverage at lowest cost over the five-year period. We performed our analysis in 5 stages, eliminating one prospective insurance plan or confirming our observations in each stage. Crystal Ball software served as an analytical tool for our analysis. The simulations conducted for our analysis consisted of 10,000 trials each. See Appendix for illustrations related to this analysis. Analysis Detail Stage 1: A comparative analysis of the maximum values of the total losses and insurance costs in the first year showed that there is only one insurance plan that guarantees that the next year losses are not going to exceed $37 million: HIC ($33.8 million maximum). RNCN1 has a maximum of $43.8 million, which is reasonably close to the $41 million limit that we are aiming to avoid in the first year. We also noted that the Self-insurance plan has minimal expected costs of $4.6 million in first year, but bears the highest volatility, which may lead to losses of up to $170.5 million (See Exhibit 1). At this stage, we exclude the RNCN2 plan from further considerations because even though is offers low expected costs, the probability of going over the limit of $37 million and incurring costs of $60 million is significant for the purposes of this analysis. We plan to...
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...Analytic functions Introduction I was interested in doing my Internal assessment in functions particularly in analytic functions as I was much fascinated with topic (functions)during the study of mathematics during the course. The theory part that includes Taylor series as well as its coverage on complex functionality. In this exploration I surveyed on the theorems associated with analytic functions as well as its functions. This has helped me widen my knowledge and mathematical skills on complex numbers, calcus and functions as topics studied during the course. I have always to kept correct justification on the theories and have used required mathematical models and correct interpretation in the results that I got in the theory processing. Analytic functions has a very wider application on Analytic modulated system whereas there is a general theory of analytic modulation system and they are developed in the transmitted signal σ(t) = Re {eiwctf(z(t)}.Due to this noticeable physical application in life, it motivated me to write a this maths exploration. In mathematics, an analytic function could be simply defined as a function that is locally given by a convergent power series. There exist two parts namely real analytic functions and complex analytic functions, functioning differently. These functions are infinitely differentiable, But as said above functions of each type are infinitely differentiable, having the complex analytic functions exhibiting properties that...
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