Math 5616H Midterm 1 with solutions Spring 2013 March 8, 2013 Total 80 points 1. (15 points) Let f (x) and g(x) be real continuous functions on an interval [a, b], such that b b f 2 (x) dx = a a b g 2 (x) dx = 1. Prove that a f (x)g(x) dx ≥ −1, and that a b f (x)g(x) dx = −1 if and only if f ≡ −g on [a, b]. Answer: Since f and g are continuous, so is (f + g)2 , which is therefore integrable. We compute: b b b b b 0≤ a b [f (x)+g(x)]2 dx = a f (x)2 dx+2 a
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coordinates of all relative extreme points of[pic]. |A)[pic] |B) [pic] |C) [pic] |D) [pic] |E) [pic] | [pic] First find the derivative of the function[pic], f ’(x): |[pic] |= |[pic] |apply power rule of differentiation | | |= |[pic] |simplify
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Three Quiz Assessment 1. four different quadratic functions: · The function f(x) is a difference of squares: * f(x) = (x+3)^2 – (2)^2) *Factored as: f(x) = (x+3+2)(x+3-2) *(x+5)(x+1) *f(x) = (x+1)(x+5) * f(x)=x^2 + 6x + 5 · The function g(x) is a sum of squares: *g(x) = (x-1)2
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The total amount of revenue made by the Miramar Resort Hotel is given by the function , , where x is the amount of money the hotel spends on advertising its services, and where both revenue and x are measured in thousands. 1. Using Wolfram Alpha, graph the revenue function over the given domain and paste the graph here. 2. Compute the marginal revenue function R'x and copy and paste a graph of this function on the domain here. Then use Wolfram Alpha to determine where revenue is increasing
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Ariana Corney Aesa McComb Mina Haw Son Writing assignment #2 When g (0) it is zero because the slope is at zero When it is g (10) it is positive because of the area being colored on the graph. The area under the x-axis is negative, so when you add all of the areas it becomes positive. That brings us to the derivative of g (x), to help us find all of the x-values, which is equal to f(x). Same with the derivative of g (a), it equals f (a), but f (a) is equal to 0. The x values are 2,4,6,8, and
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QUESTION 1 Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function. Rises to the left, falls to the right Rises to the right, rises to the left Falls to the left, rises to the right Falls to the right QUESTION 2 Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function. f(x) = 4×2 – 5x + 4 Falls to the left, rises to the right Falls to the left, falls to the right Rises to the left
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NR 451 ENTIRE COURSE DEVRY To purchase this visit following link: http://www.activitymode.com/product/nr-451-entire-course-devry/ Contact us at: SUPPORT@ACTIVITYMODE.COM NR 451 ENTIRE COURSE DEVRY NR 451 Milestone 1 PICO Evidence Guidelines NR 451 Milestone1 PICO Evidence Worksheets NR451 Milestone 2 Desig _Proposal Interlicchio NR 451 Power Point Presentation- Capstone 1 NR 451 Power Point Presentation- Capstone 2 NR 451 Week 1 and Week 2 Discussions Latest 2015 NR 451 Week 3 and Week
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_______________________________________________________ Dr. Xiaobo Zhou Date Table of Contents Online E-Voting System Project Documentation 4 Abstract 6 1. Introduction 7 2. E-Voting System Related Literature 9 2.1. Public Key Cryptography 9 2.2. Homomorphic Encryption 10 2.3. Zero Knowledge Proofs 10 2.4. Threshold Cryptography 10 2.5. Cryptographic Voting Protocol 11 2.6. Issues in secure e-voting system 12 2.7. Completely Automated Public Turing test
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RSA Key Extraction via Low-Bandwidth Acoustic Cryptanalysis∗ Daniel Genkin Technion and Tel Aviv University danielg3@cs.technion.ac.il Adi Shamir Weizmann Institute of Science adi.shamir@weizmann.ac.il Eran Tromer Tel Aviv University tromer@cs.tau.ac.il December 18, 2013 Abstract Many computers emit a high-pitched noise during operation, due to vibration in some of their electronic components. These acoustic emanations are more than a nuisance: they can convey information about the
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What is a Keypad? A keypad is a set of buttons or keys bearing digits, symbols and/or alphabetical letters placed in order on a pad, which can be used as an efficient input device. A keypad may be purely numeric, as that found on a calculator or a digital door lock, or alphanumeric as those used on cellular phones. Explanation for Keypad Aside from the row of number keys found on the upper portion of a computer keyboard, a separate numerical pad is also located on the right side for efficient
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