construct the polynomial function‚ f(x)‚ that will be the path of your roller coaster. Show all of your work. Answer: To create the polynomial function‚ we would need to find the three roots to create factors. The roots would be the x-coordinates‚ 6‚ -2‚ and -7 so the factors are x-6‚ x+2 and x+7. Now multiple x-6 and x+2 to get x^2-4x-12. Take that answer and multiply it by the third factor‚x+7 and it would result with x^3+x^2-28x-12x-84. Combine like terms and the polynomial function is f(x) = x^3+x^2-40x-84
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DURATION : 60 minutes ANSWER ALL QUESTIONS. 1. Given the function f ( x‚ y ) = x 2 + 2 y 2 − 1 a. Find the domain and range of the function. (2 marks) b. Sketch the contour map of the function f ( x‚ y ) using three level curves‚ c = 1‚ 2‚ 3 . (4 marks) c. Use 3D-contour map to sketch roughly the surface of f ( x‚ y ) . (2 marks) 2 4 x2 − y 2 ‚ x2 + 2 y 2 f ( x‚ y ) along x- axis and y-axis‚ Given the function f ( x‚ y ) = a. find the lim ( x ‚ y )→(0‚0) (4 marks) b. does
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Lecture 6: Function. Limits and continuity. Plan: 1) Concept of function. Basic properties of functions. 2) Elementary functions. Classification of functions. 1) Concept of function. Basic properties of functions. Definition 1. If to each element x of set X () is put in conformity the element y of set Y () speak‚ that on set X function is given. Where х is an independent variable (or argument)‚ y - a dependent variable‚ and the letter f designates the law of conformity. Set X is
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definitions. For EC201 • Nonsatiation means that utility can be increased by increasing consumption of one or both goods. If the utility function is differentiable you should test for nonsatiation by finding the partial derivatives of the utility function. 1.1.2 Example: testing for convexity with a Cobb-Douglas utility function A Cobb-Douglas utility function has the form u(x1 ‚ x2 ) = xa xb where a > 0 and b > 0. Here u(x1 ‚ x2 ) = 12 2/5 3/5 x1 x2 . Assuming that x1 > 0 and x2 > 0 the partial
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# the start of this has the power-law fitting function you can use‚ make sure to evaluate it before calling plfit # PLFIT fits a power-law distributional model to data. # # PLFIT(x) estimates x_min and alpha according to the goodness-of-fit # based method described in Clauset‚ Shalizi‚ Newman (2007). x is a # vector of observations of some quantity to which we wish to fit the # power-law distribution p(x) ~ x^-alpha for x >= xmin. # PLFIT automatically detects whether x is
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Code] Figure (2): Verification of Two Point Method in Time domain Figure (3): Verification of Two Point Method in Frequency domain (b) Log Method For this method‚ we need samples of the output which can be done using Matlab‚ the following function takes samples every 1 second starting from 1 to 20‚ and the results are stored in arrays x and y. [See Appendix-B for MATLAB Code] Figure (4): Log method curve From the graph‚ we can get cross-axis value. Thus: K=1‚ L/T=0.9081‚ L=1.89
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Math 135 Final Exam Study Guide The graph of a function is given. Follow the directive(s). 1) y 5 (0.5‚ 2) (3.5‚ 2) 5 (6‚ -1.1) x -5 (-5‚ -3) (-4‚ -3) -5 (a) List all the intervals on which the function is increasing. (b) List all the intervals on which the function is decreasing. (c) List all the intervals on which the function is constant. (d) Find the domain. (e) Find the range. (f) Find f(-5). (g) Find f(6). (h) Find x when f(x) = 0. (i) Find the x-intercept(s). (j) Find the y-intercept(s)
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Previous exam questions on area between functions and volumes of solids. 1. Let f(x) = cos(x2) and g(x) = ex‚ for –1.5 ≤ x ≤ 0.5. Find the area of the region enclosed by the graphs of f and g. (Total 6 marks) 2. Let f(x) = Aekx + 3. Part of the graph of f is shown below. The y-intercept is at (0‚ 13). (a) Show that A =10. (2) (b) Given that f(15) = 3.49 (correct to 3 significant figures)‚ find the value of k. (3) (c) (i) Using your value of k‚ find f′(x). (ii) Hence
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→0 + ( 2. (3 marks) Find the derivative of y = 3 x + 5 2 ) sec x Calculus I Midterm 2 November 2013 3 3. (Total 8 marks) Answer each question in the space provided. Do NOT simplify your answer. x2 − x 3 dy of the function f ( x) = ln( x3 ) a) Find dx e [ ( )] b) If f ( x) = arcsin x c) Find ( ( d sin 2 dx d) If f ( x) = 1 4 x 3 4 + π 2 ‚ find f ′(x) tanh (x ) + (2 x ) )) 1 −e 2 (2 marks) (2 marks)
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FISH PRODUCTION - MODELING The aim of this investigation is to consider commercial fishing in a particular country in two different environments‚ that is from the sea and a fish farm (aquaculture). The following data provided below was taken form the UN Statistics Division Common Database. The tables gives the total mass of fish caught in the sea‚ in thousands of tones (1 tone = 1000 kilograms). Year | 1980 | 1981 | 1982 | 1983 | 1984 | 1985 | 1986 | 1987 | 1988 | Total Mass | 426
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