Answered: Given the function f , g and h, all…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The table gives heavy - metal nuclear waste (in thousands of metric tons) from spent reactor fuel now stored temporarily at reactor sites, awaiting permanent storage. Waste y Year x 1995 32 2000 42 2010 61 2020 76 Let x = 0 represent 1995, x = 5 represent 2000 (since 2000 - 1995 = 5), and so on. a) For 1995, the ordered pair is (0, 32). Write the ordered pair for the data for the other years given in the table. b) Plot the ordered pairs (x,y). Do the points lie approximately in a straight line? c) Use the ordered pairs (0, 32) and (25, 76) to find the equation of a line that approximates the other ordered pairs. Write the equation in slope - intercept form and in standard form. d) Use the slope - intercept equation form from part (c) to estimate the amount of nuclear waste in 2005.
1. Let f(x, y) =x+2y. Find f(0, 1), f (2, –1), f(a, a), and f(a + h, b) – f(a, b). 2. Let f(x, y) = xy². Find the respective values of f (0, 1), f(-1,2), f(104, 10-2), f (a, a), f(a+h, b), and f(a, b+ k) – f (a, b). %3D 3. Let f(x, y) = 3x² – 2xy+ y. Find f(1, 1), f(-2, 3), ƒ(1/x, 1/y), p = [f(x+h,y) – f(x, y)]/h, and q = [f(x, y + k) – f(x, y)]/k. %3D SECTION 11.2 / PARTIAL DERIVATIVES WITH TWO VARIABLES 411 4. Let f(x, y) = x² + 2xy + y². (a) Find f(-1,2), f(a, a), and f (a + h, b) – f(a, b). (b) Prove that f(2x, 2y) = 2f(x, y), and that f(tx, ty) = tf(x, y) for all t.
Teachers get courses assigned to teach each semester. For each instructor, there are the courses that the instructor can teach based on the skill set of the instructor, and there are courses that the teacher would rather teach all the time, closer to their specialization. To be able to teach in any department, a teacher must be able to teach more than the favorite courses. Let X denote the proportion of teachers who teach the whole spectrum of courses taught in a department, and Y the proportion of teachers who teach the courses they specialize in. Let X and Y have the joint density function : f(x,y)=2(x+y),0<y<x<1 (a) Given that 10% of the teachers teach the whole spectrum of courses, what is the probability that fewer than 5% teach their favorite courses? (b) What is the expected percentage of teachers teaching their favorite courses when the proportion of teaching the whole spectrum is 0.7?

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Given the function f , g and h, all with source and target {1, 2, 3, 4}, defined as follows: f ={(1,2),(2,4),(3,1),(4,3)} g = {(1, 3), (2, 3), (3, 4)} h = {(1, 1), (2, 2), (3, 3), (4, 4)} 1.Which of f , g , and h are total functions, and which are partial? Evaluate 1. g(2) 2. f (f (4)) 3. g (h(4))