technology generated by a production function f(x) = x2 . The production set is Y = {(y‚ −x) : y ≤ x2 } which is certainly not convex‚ but the input re√ quirement set is V (y) = {x : x ≥ y} which is a convex set. 1.2 It doesn’t change. 1.3 1 = a and 2 = b. 1.4 Let y(t) = f(tx). Then dy = dt so that 1 dy 1 = y dt f(x) 1.5 Substitute txi for i = 1‚ 2 to get f(tx1 ‚ tx2 ) = [(tx1 )ρ + (tx2 )ρ ] ρ = t[xρ + xρ ] ρ = tf(x1 ‚ x2 ). 1 2 This implies that the CES function exhibits constant returns to
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Even & Odd Functions 2 Algebraic Definition 2 Graphic Definition 4 Combining Even & Odd Functions 6 Multiplication 6 Addition 7 Integrals of Even & Odd Functions 7 Fourier Series: Even & Odd Functions 9 Arbitrary Period (2L) 9 Case of Period 2π 10 References 14 Algebraic Definitions 1) Even Function: 2) Odd Function: Algebraically You may be asked to "determine algebraically" whether a function is even or odd. To do this‚ you take the function and plug
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COMPOSITION AND INVERSE FUNCTIONS Composition and Inverse Functions Kimberly Harris MAT 222 Week 5 Assignment Instructor: Donna Wall July 18‚ 2014 Composition and Inverse Functions In this week’s assignment I am given three Composition and Inverse Functions. Functions gives an opportunity for manipulating experiences using different values. What these values does is to help business owners and others the opportunity to compare rates and dates. Functions can extend independent
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Real World Quadratic Functions Maximum profit. A chain store manager has been told by the main office that daily profit‚ P‚ is related to the number of clerks working that day‚ x‚ according to the function P = −25x2 + 300x. What number of clerks will maximize the profit‚ and what is the maximum possible profit? In order to find the point at which profit is maximized‚ I must find the critical points of the first derivative of the equation. Coefficient of x^2 is negative‚ so
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Using Polynomials in the “Real World” Polynomial functions are used in our everyday lives in a few different ways‚ this includes art‚ architecture‚ construction‚ financial planning‚ and manufacturing. We can also calculate how long it will take one person to do a job alone when we know how long it takes a group to get it done as well. Farmers on crop farms work dawn to dusk through the growing season to produce the grains‚ fruits‚ and vegetables that feed the country. These equations help them
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which contains set of equations that represent objective function and constraints. The keywords in this article are Objective Function and Constraints‚ according to Heizer & Render (2008) Objective Function are mathematical expression expressed in linear programming designed to maximizes or minimizes some quantity‚ for example profit can maximized while the cost might be reduced. The objective function is also called effectiveness function‚ it is the mathematical expression of the objectives which
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Singularity functions 1-2-1 The unit-step function The continuous-time unit-step function The continuous-time unit-step function is denoted as u ( t ) and is defined mathematically by: 0‚ u (t ) = 1‚ for t < 0 for t ≥ 0 which have the zero amplitude for all t < 0 and the amplitude of 1 for all t ≥ 0 ‚ and its plot is shown in Figure 1-10 u (t ) 1 0 t 2 Fundamental of signal processing Figure 1-10: The continuous-time unit step function The discrete-time unit-step function The
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Submitted By: Ma. Karla Rachelle Ulibas Student Submitted To: Mr. Ray-ann Buenafe Instructor HISTORY OF TRIGONOMETRIC FUNCTIONS Trigonometric functions seem to have had their origins with the Greek’s investigation of the indirect measurement of distances and angles in the “celestial sphere”. (The ancient Egyptians had used some elementary geometry to build the pyramids and remeasure lands flooded by the Nile‚ but neither they nor the ancient Babylonians had developed the concept of
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Boolean Functions - Computer Organization (IT 25) BOOLEAN FUNCTIONS A Boolean function consists of a binary variable denoting the function‚ an equals sign and an algebraic expressions formed by using binary variables the constants 0 and 1‚ the logic operation symbols‚ and parentheses. For a given value of the binary variables‚ Boolean function can be equal to either 1 or 0. Example: F = X + Y’Z The two parts of the expression X and Y’Z‚ are called terms of the function F. The function F is
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Quadratic Function MCR3U1 (Nature of the Roots) MINDS ON... The demand to create automotive parts is increasing. BMW developed three different methods to develop these parts. The profit function for each method is given below‚ where y is the profit and x is the quantity of parts sold in thousands: PROCESS A: P(x) = -0.5x2 + 3.2x –5.12 PROCESS B: P(x) = -0.5x2 + 4x – 5.12 PROCESS C: P(x) = -0.5x2 + 2.5x – 3.8 The graphs of the corresponding profit functions are shown
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