[12 marks] Using the definition of big-O, show that f(x) is big-O of g, where: f(x)...
QUESTION 3 To show that f(x) is O(g(x) using the definition of big o, we find Cand k such that f(x) < Cg(x) for all x > k. QUESTION 4 Finding the smallest number in a list of n elements would use an OU) algorithm.
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark 1729 is O(1) b) 3 marks 2n2-4n -3 is O(n2) 2. [3 marks] Using the definition of Big-Oh, prove that 2n2(n 1) is not O(n2) 3. 6 marks Let f(n),g(n), h(n) be complexity functions. Using the definition of Big-Oh, prove the following two claims a) 3 marks Let k be a positive real constant and f(n) is O(g(n)), then k f(n) is O(g(n)) b)...
State the definition of “f(x) is O(g(x))” and use the definition to show that x 2 + 3x is O(x 3 ). Please show as much work as possible. Thanks.
#1. Using the definition of big-O, prove that f(x) = 5x^4+x^3+8x-2 . Show all work. #2. void bubbleSort(Student myClass[], int size) { int pass = 0; // counts each pass of the sort bool done = false; // whether sorted or not // each pass puts one element into its sorted position, // smallest value bubbles to the top of the array while (!done) { done = true; // possibly sorted // compare consecutive elements, swap if out of order...
(a) Let f(x) = 3x – 2. Show that f'(x) = 3 using the definition of the derivative as a limit (Definition 21.1.2). 1 (b) Let g(x) = ? . Show that y that -1 g'(x) = (x - 2)2 using the definition of the derivative as a limit (Definition 21.1.2).
Use the definition of the fact that f(x) is O(g(x)) to show that: 1. 7x^2 is O(x^2) 2. x^4 + 9x^3 + 4x + 7 is O(x^4) 3. (x^2+1) / (x+1) is O(x) Hint: Try to simplify algebraic expression.
(5) The following is the formal definition for O-notation, written using quantifiers and variables: f(x) is (g(x)) if, and only if, 3 positive real numbers k and C such that Vu > k, |f(x) <C|g(2) Write the negation for the definition using the symbols V and 3.
Formal Definitions of Big-Oh, Big-Theta and Big-Omega: 1. Use the formal definition of Big-Oh to prove that if f(n) is a decreasing function, then f(n) = 0(1). A decreasing function is one in which f(x1) f(r2) if and only if xi 5 r2. You may assume that f(n) is positive evervwhere Hint: drawing a picture might make the proof for this problem more obvious 2. Use the formal definition of Big-Oh to prove that if f(n) = 0(g(n)) and g(n)...
2. (5) The following is the formal definition for O-notation, written using quantifiers and variables: f(x) is (g(x)) if, and only if, 3 positive real numbers k and C such that Vr > k, f(x) <C|g(x)]. Write the negation for the definition using the symbols V and ).
32 points Prove each of the following statements by applying the definition of Big-O. That is, derive an inequality (show your work) and identify the witness constants C and k as per the definition of Big-O.