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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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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3.3 Derivatives of Trigonometric Functions Math 1271‚ TA: Amy DeCelles 1. Overview You need to memorize the derivatives of all the trigonometric functions. If you don’t get them straight before we learn integration‚ it will be much harder to remember them correctly. (sin x) = cos x (cos x) = − sin x (tan x) = sec2 x (sec x) = sec x tan x (csc x) = − csc x cot x (cot x) = − csc2 x A couple of useful limits also appear in this section: lim
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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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Properties of Trigonometric Functions The properties of the 6 trigonometric functions: sin (x)‚ cos (x)‚ tan(x)‚ cot (x)‚ sec (x) and csc (x)are discussed. These include the graph‚ domain‚ range‚ asymptotes (if any)‚ symmetry‚ x and y intercepts and maximum and minimum points. Sine Function: f(x) = sin (x) * Graph * Domain: all real numbers * Range: [-1 ‚ 1] * Period = 2pi * x-intercepts: x = k pi ‚ where k is an integer. * y-intercepts: y = 0 * Maximum points: (pi/2
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of the equation. Be sure to show all of your work. Describe how you would graph this line using the slope-intercept method. Be sure to write in complete sentences. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences. Graph the function using one of the following two options below. On the graph‚ make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work. You may graph your
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sports event estimates that if the event is announced x days in advance‚ the revenue obtained will be R(x) thousand $ where R(x) = 400 + 120x - x2. The cost of advertising event for x days is C(x) thousand $‚ where C(x) = 2x2+300. a) Find profit function P(x) =R(x) – C(x) & sketch graph. b) How many days in advance should the event be announced in order to maximize profit. What is the max profit? c) What is the ratio revenue to cost Q(x) =R(x)C(x) at the optimal announcement time found
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Sine‚ Cosine‚ and Tangent Functions Essential Questions: What is a function? How is the sine definition different from the sine function? Cosine? Tangent? From the graph of these functions‚ list some properties that describe them? Rebecca Adcock‚ a former student of EMAT 6690 at The University of Georgia‚ and I agree that the concept of the Sine‚ Cosine Functions will occur at lesson 6 of a beginning trigonometry unit. I praise her and her work because I want to use her thoughts on this particular
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TAGUCHI LOSS FUNCTION EXAMPLE PROBLEMS 1. A blueprint specification for the thickness of a dishwasher part at Partspalace‚ Inc. is0.325 ± 0.025 centimeters (cm). It costs $10 to scrap a part that is outside thespecifications. Determine the Taguchi loss function for this situation. 2. A team was formed to study the dishwasher part described in Problem 1. Whilecontinuing to work to find the root cause of scrap‚ they found a way to reduce the scrapcost to $5 per part. a. Determine the Taguchi loss
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PROPERTIES OF SINE AND COSINE FUNCTIONS: 1. The sine and cosine functions are both periodic with period 2π. 2. The sine function is odd function since it’s graph is symmetric with respect to the origin‚ while the cosine function is an even function since it’s graph is symmetric with respect to y axis. 3. The sine functions: a. Increasing in the intervals[0‚ π/2]and [3π/2‚ 2π]; and b. Decreasing in the interval [π/2‚ 3π/2]‚over a period of 2 π. 4. The cosine function is: a. Increasing in the interval
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