10.2. Need for hidden line and surface elimination algorithms When we attempt to view a picture that contains some non-transparent things or surfaces, then those objects or surfaces are hidden from us i.e. we cannot view those parts that are behind the objects that we can see. We should remove such hidden surfaces to get a realistic view of an image. Hidden surface problem is a process in which we identify and remove the hidden surfaces of a picture as shown in figure 10.1. Objects in computer
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Week 1 Linear Functions * As you hop into a taxicab in Kuala Lumpur, the meter will immediately read RM3.30; this is the “drop” charge made when the taximeter is activated. After that initial fee, the taximeter will add RM2.40 for each kilometer the taxi drives. In this scenario, the total taxi fare depends upon the number of kilometer ridden in the taxi, and we can ask whether it is possible to model this type of scenario with a function. As you hop into a taxicab in Kuala Lumpur, the meter
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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
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Excel Functions Every Community Manager Should Know Tips for data manipulation from our Analysts Excel Functions Every Community Manager Should Know Tips for data manipulation from our Analysts Excel can be intimidating Let’s face it, without functions Excel is just a wonderful way to store information. With functions, however, Excel becomes an amazing tool for manipulating and making sense out of large amounts of data. That’s why we love Excel so much. With a few little functions we can take
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Managerial Mathematics(QQM 1023) Tutorial 2 – Introduction to Function 1. Which of the following equations define y as a function of x? a) y = 3x + 1 b) y = 2x2 c) y = 5 d) y = 2x e) x = 3 f) y2 = x g) y = x3 h) y = [pic] i) y = x j) y = [pic] 2. Determine types of function for the following equations: a) f(x) = 2 b) g(x) = [pic] c) f(x) = 4 – x d) f(x) = 2x e) g(x) = x2 + 3x f) h(x) = 2x
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Contents 0. Preface 1. Functions and Models 1.1. Basic concepts of functions 1.2. Classification of functions 1.3. New functions from old functions 1 2 2 5 8 0. Preface Instructor: Jonathan WYLIE, mawylie@cityu.edu.hk Tutors: Radu Gogu, rgogu2@student.cityu.edu.hk. Texts: Single Variable Calculus, by James Stewart, 6E. In this semester, we will cover the majority of Chap 1-4, 7, 12. Upon completion of this course, you should be able to understand limit, derivatives, and its applications in mathematical
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Honors Algebra II Supplemental Notes Oblique Asymptotes Key Concepts: An oblique asymptote is an oblique, or slanted, line that the graph of a function approaches, but never touches, as x → ∞ ( x approaches infinity). To find the oblique asymptote of a rational function: 1. Reduce the rational function P( x) to lowest terms. An oblique asymptote can be found Q( x) when the degree of P ( x) is one greater than the degree of Q ( x ) . c 2. Divide P ( x) by Q ( x ) using long division to get
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the set of integers and[pic]. F(x) is a one-to-one function if we can show that: For [pic] and[pic], [pic]=[pic]===> [pic]=[pic] Let’s find out: [pic]==> [pic]=[pic], and [pic]=[pic] So, [pic]=[pic]==> [pic]=[pic]. Subtracting 101 on both sides gives [pic]==> [pic]=[pic]. Since we’re able to show that [pic]=[pic] ==> [pic]=[pic], we then conclude that [pic] is a one-to-one function. 2. Let’s prove that [pic] is a one-to-one function. To prove that, we have to show that For [pic] and[pic]
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small and simple circuits • Express a switching function of n variables as a composition of switching functions of less than n variables Motivation: • Reduce the complexity of simplification • Reduce the size of a circuit by finding common circuit elements Theoretical background: • Shannon’s Expansion Theorem (SET): – Simple type of decomposition – f(x1, x 2, ..., xn) = x 1f(1, x 2, ..., xn) + x’1 f(0, x 2, ..., xn) 1 Residues • The function that is obtained from setting one of the variables
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some Maple work. 1. Solve the following inequalities: a) b) c) 2. Appendix D #72 3. Consider the functions and . a) Use a Maple graph to estimate the largest value of at which the graphs intersect. Hand in a graph that clearly shows this intersection. b) Use Maple to help you find all solutions of the equation. 4. Consider the function. a) Find the domain of. b) Find and its domain. What is the range of? c) To check your result in b), plot and
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