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This document provides an overview of differential calculus concepts including: 1) Differential calculus deals with finding exact derivatives directly from a function's formula without using graphs. It examines the rate of change of one quantity with respect to another. 2) Key concepts covered include derivative rules, the product rule, quotient rule, derivatives of trigonometric functions, and the squeeze/sandwich theorem. 3) Real-life applications of differential calculus include calculating profit/loss, rates of change like temperature, deriving physical equations, and calculating speed or distance over time.

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APLICACIONES DE LA DERIVADA EN LA CARRERA DE (Mecánica, Electrónica, Telecomu...

APLICACIONES DE LA DERIVADA EN LA CARRERA DE (Mecánica, Electrónica, Telecomu...

derivativesanditssimpleapplications-160828144729.pptx

derivativesanditssimpleapplications-160828144729.pptx

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APLICACIONES DE LA DERIVADA EN LA CARRERA DE (Mecánica, Electrónica, Telecomu...

APLICACIONES DE LA DERIVADA EN LA CARRERA DE (Mecánica, Electrónica, Telecomu...WILIAMMAURICIOCAHUAT1

El cálculo diferencial proporciona información sobre el comportamiento de las funciones
matemáticas. Todos estos problemas están incluidos en el alcance de la optimización de funciones y pueden resolverse aplicando cálculoderivativesanditssimpleapplications-160828144729.pptx

The document discusses derivatives and their applications. It begins by introducing derivatives and defining them as the rate of change of a function near an input value. It then discusses rules for finding derivatives such as the constant multiple rule, sum and difference rules, product rule, and quotient rule. Examples are given to illustrate applying these rules. The document also covers composite functions, inverse functions, second derivatives, and applications of derivatives in physics for problems involving velocity and acceleration.

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This document discusses the application of calculus derivatives in the career of geospatial technologies. It begins with introducing the concept of the derivative and its calculation. It then discusses the criteria of the first and second derivatives, which can be used to find relative extremes of a function. Three practice exercises are included, relating to optimization problems that can be solved using derivatives. Graphs of the exercises are generated in Geogebra. The document emphasizes how derivatives can be useful for tasks like optimizing processes in geospatial technologies applications.

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Aplicaciones de la derivadas en contabilidad

This document discusses the application of derivatives in accounting. It begins with introducing derivatives and their uses in economics and accounting. Specifically, derivatives represent a useful tool for calculating marginal costs, revenues, profits, and production. The document then presents two examples demonstrating how to use derivatives to find total cost, marginal cost, maximum and minimum prices, and average cost in accounting scenarios. It concludes that derivatives are a 100% useful tool that can simplify complex calculations and processes, with many applications in economics and accounting.

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On the discretized algorithm for optimal proportional control problems constr...

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poster2

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1) The document presents a theoretical analysis of the application of derivatives to problems that may arise in biotechnology and electronics careers.
2) It provides examples of using derivatives to find maximums and minimums, such as maximizing tree growth or signal coverage.
3) The analysis covers the geometric interpretation of derivatives, criteria for finding extremes using the first and second derivatives, and applies these concepts to sample problems involving quadratic functions.

Grupo#5 taller parcial 2

1) The document presents a theoretical analysis of the application of derivatives to problems that may arise in biotechnology and electronics careers.
2) It provides examples of using derivatives to find maximums and minimums, such as maximizing tree growth or signal coverage.
3) The analysis includes the geometric interpretation of derivatives, criteria for using the first and second derivatives to find critical points and determine if they are maximums or minimums.

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3. One example works through applying the chain rule to find df/dt for the function f(x,y) = x^2 + y^2, where x = t^2 and y = t^4, and verifies the

Calculus

This document discusses derivatives, including their definition, history, real-life applications, and use in various sciences. Derivatives are defined as the instantaneous rate of change of one variable with respect to another and geometrically as the slope of a curve at a point. Their modern conception is credited to Isaac Newton and Gottfried Leibniz in the 17th century. Derivatives have applications in business for estimating profits and losses, and in automobiles to calculate speed and distance traveled from odometer and speedometer readings. They are also used in physics to define velocity and acceleration and in mathematics to study extreme values, mean value theorems, and curve sketching.

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This presentation introduces regression analysis. It discusses key contributors to the development of regression analysis. It also provides an overview of different types of regression models, including simple linear regression, multiple regression, and nonlinear regression. Examples are provided to demonstrate calculating regression equations using the method of least squares from raw data and data with means removed.

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K0737781

This document describes the design of a decoupler for an interacting two-tank system. The dynamic behavior of the system was studied using a mathematical model and experimentally by introducing step changes to the inlet flow rates. Relative gain array (RGA) analysis showed interaction between the liquid level controls and inlet flow rate manipulations. To reduce this interaction, decoupler blocks were designed with transfer functions that cancel the effect of one manipulated variable on the other controlled variable. Experimentally measured and theoretically calculated RGA values matched, validating the decoupler design approach. The decoupler was found to lessen interaction and allow independent control of liquid levels in each tank despite interactions in the physical process.

A Study of Some Systems of Linear and Nonlinear Partial Differential Equation...

In this paper, we introduce the solution of systems of linear and nonlinear partial differential equations subject to the initial conditions by using reduced differential transformation method. The proposed method was applied to three systems of linear and nonlinear partial differential equations, leading to series solutions with components easily computable. The results obtained are indicators of the simplicity and effectiveness of the method

APLICACIONES DE LA DERIVADA EN LA CARRERA DE (Mecánica, Electrónica, Telecomu...

APLICACIONES DE LA DERIVADA EN LA CARRERA DE (Mecánica, Electrónica, Telecomu...

derivativesanditssimpleapplications-160828144729.pptx

derivativesanditssimpleapplications-160828144729.pptx

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Taller parcial 2

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CALCULUS 2.pptx

Aplicaciones de la derivadas en contabilidad

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CHAPTER 7.pdfdjdjdjdjdjdjdjsjsjddhhdudsko

CHAPTER 7.pdfdjdjdjdjdjdjdjsjsjddhhdudsko

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On the discretized algorithm for optimal proportional control problems constr...

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mas-150813232504-lva1-app6892.pdf

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evs ppt (2).pptx

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maths diff.calculus ppt (1).pptx

This document provides an overview of differential calculus concepts including:
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ranjithreddy123-220304124409.pdf

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Uniform and exponential distribution ppt

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mas-150813232504-lva1-app6892.pdf

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Girls Call Chennai 000XX00000 Provide Best And Top Girl Service And No1 in City

Updated Limitations of Simplified Methods for Evaluating the Potential for Li...

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In this talk, we will share our experiences to explain why state-of-art systems offer poor abstractions to tackle such workloads and why they suffer from poor cost-performance tradeoffs and significant complexity.
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Enabling business users to directly query their data sources is a significant advantage for organisations.
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Introduction And Differences Between File System And Dbms.pptx

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Technical Seminar of Mca computer vision .ppt

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FINE-TUNING OF SMALL/MEDIUM LLMS FOR BUSINESS QA ON STRUCTURED DATA

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- 1. DIFFERENTIAL CALCULUS BATCH-6: 1. VANATHI.S 2. VARSHINIE.A.L 3. SRIRAM.R 4.THIRUNAVUKARASU.S 5. VISHAL.S 6. SURANJANA.N.S >>> ENGINEERING MATHEMATICS
- 2. TABLE OF CONTENTS 1. INTRODUCTION 2. BAKING ANALOGY 3. DIFFERENTIAL CALCULUS 4. DERIVATIVE RULES 5. PRODUCT RULE 6. QUOTIENT RULE 7. DERIVATIVE OF TRIGNOMETRIC FUCTIONS 8. THE SANDWICH/SQUEEZE THEOREM 9. CONCLUSIONS
- 3. INTRODUCTION >> Differential calculus is a procedure for finding the exact derivative directly from the formula of the function without having to use graphical methods. >> It is a method that deals with the rate of change of one quantity with respect to another.
- 4. BAKING ANALOGY >> In this we will focus on the formulas and rules for both differentiation, the method by which we calculate the derivative of a function. >> Before we dive into formulas and rules for differentiation , let’s look at some notations for differentiation. >> we can write f(X) as d/dx f(x),f’(x),df(x) and Df(x) We read these as d by dx of f of x, f’ prime of f of x, df of x and cap Df of x.
- 5. DIFFERENTIAL CALCULUS >> Differential calculus is the area of calculus dealing with cutting something into smaller pieces in order to analyze how it changes. >> The primary operation of differential calculus is the derivative. The derivative of a function given the infinitesimal change of the function with respect to one of it’s variable. >> The derivative represents the slope of function at every point it is defined.
- 6. DERIVATIVE RULES LOGARITHMIC FUNCTIONS (d/dx): 1. e^x = e^x 2. a^x = a^x ln(a) 3. Ln(x) = 1/x 4. Log a ^x = 1/xln(a) TRIGONOMETRIC FUNCTIONS (d/dx): 1. Sin(x)= cos(x) 2. Cos(x)= -sin(x) 3. Tan(x)= sec^2(x) 4. Cosec(x)= - cosec(x) cot(x) 5. Sec(x)= sec(x) tan(x) 6. Cot(x)= -cosec^2(x)
- 7. Real life applications of differential calculus: >> Calculation of profit or loss with respect to business using graphs. >> Calculation of rate of change of temperature. >> To derive many physical equations. >> Calculation of speed or distance covered such as miles per hour , km/hour.
- 8. PRODUCT RULE >> The derivative of the product of two differentiable functions is equal to the addition of the first multiplied by the derivative of the second and the second function multiplied by the derivative of the first function. APPLICATION: 1. The product rule is used in calculus, when you are asked to take derivative of the function. 2. It makes calculation clean and easier to solve. 3. It is used to differentiate product of two or more functions.
- 9. DERIVATIVE PRODUCT RULE If u and v are differentiable at x, then so is their product uv and d/dx(u.v) = u (dv/dx) +v (du/dx) Example: Q) Find the derivative of y=(x^2 +1)(x^3+3) Answer: d/dx(x^2+1)(x^3+3)=(x^2+1)(3x^2)+ (2x)(x^3+3) =3x^4+3x^2+2x^4+6x =5x^4+3x^2+6x The particular product can be differentiated as well by multiplying out the original expression for y and differentiating the resulting polynomial. Y=(x^2+1)(x^3+3)=x^5+x^3+3x^2+3 dy/dx=5x^4+3x^2+6x This is in agreement with our first calculation.
- 10. QUOTIENT RULE >> A quotient rule is similar to product rule. A quotient rule is stated as the ratio of the quantity of the denominator times the derivative of the numerator function minus the numerator times the derivative of the denominator function to the square of the denominator function. APPLICATION: 1. It is used for finding the derivative of a quotient of functions. 2. It is used for extend the power rule to functions with negative exponents. 3. To combine differentiation rule to find the derivative of a polynomial or rational function.
- 11. DERIVATIVE QUOTIENT RULE If u and v are differentiable at x and if v(x) is not equal to 0 then the quotient u/v is differentiable at x and d/dx(u/v)= v (du/dx) – u (dv/dx)/ v^2 Example: Q)Find the derivative of y=(t^2-1)/(t^3+1) Answer: u=t^2-1 v=t^3+1 dy/dt=(t^3+1).2t- (t^2-1).3t^2/(t^3+1)^2 =2t^4+2t-3t^4+3t^2/(t^3+1)^2 =-t^4+3t^2+2t/(t^3+1)^2
- 12. SQUEEZE THEOREM >> In calculus the squeeze theorem is a theorem regarding the limit of a function that is trapped between two other function. >> The squeeze theorem is used in calculus and mathematical analysis typically to confirm the limit of a function via comparison with other function whose limits are known. >> If the right hand limits and left hand limits do not equal eachother we cannot utilize squeeze theorem. If f(x)<g(x)<h(x) when x is near a If limxa f(x)=limxa h(x)=L then limxa g(x)=L.
- 13. WHY IS IT CALLED SANDWICH THEOREM? >> The squeeze theorem is also called as sandwich or pinching theorem. It is a way to find the limit of one function if we know the limits of two functions it is “sandwiched” between. APPLICATION: It is used for calculating the limit of a given trigonometric funtions.
- 14. EXAMPLE OF SANDWICH THEOREM Q) Using sandwich theorem show that: limx0 x^2 sin (1/x)=0 ANSWER: Let -1<sin(1/x)<1 Multiply by x^2 -x^2<x^2 sin 1/x <x^2 Lim x0 (–x^2)<lim x0 x^2 sin (1/x)< lim x0 x^2 Lim x->0 (-x^2)=-0=0 Lim x x^2=0=0 Lim x0 (-x^2)= lim x (x^2) Lim x0 x^2 sin (1/x)=0
- 15. THANK YOU!