For each function defined below, find the value of k such that s(n) = O(n). For...
1. For each function defined below, find the value of k such that s(n) = O(nk). For part (a), justify your answer from the definitions of O, O, and by finding explicit constants that work, following the examples in Proofs 7.2.1 and 7.2.3 in the zyBook. Don't just refer to Theorem 7.2.2. For part (b), you do not need to find explicit constants, just explain why your answer is correct. (a) s(n) = (2n + 1)(5n2+1) (b) s(n) = nºt(n)...
Q1 (4 points) Assume that f: NXN N is a function defined by f(n, k) = 2n+l(4k + 3). Is an injective function? Justify your answer. + Drag and drop your images or click to browse...
n=2 Question 3 3 pts Find the Fourier Sine series for the function defined by 0<c<n f() = { 0, 2n, n<3 < 2n and write down, 1. The period T and the frequency wo of the Fourier Sine series 2. The coefficients bn for n = 1,2,3,...
Need to find number of elementary expressions in terms of n, not looking for Big O complexity. 4. Work out the number of elementary operations in the worst possible case and the best possible case for the following algorithm (justify your answer): 0: function Nonsense (positive integer n) 1: it1 2: k + 2 while i<n do for j+ 1 to n do if j%5 = 0 then menin else while k <n do constant number C of elementary operations...
Q6) let T(n) be a running time function defined recursively as 0, n=0 n=1 3T(n - 1)- 2T(n - 2), n> 1 a) Find a non-recursive formula for T(n) b) Prove by induction that your answer in part (a) is correct. c) Find a tight bound for T(n).
(2) For an integer n, let Z/nZ denote the set of equivalence classes [k) tez: k -é is divisible by n (a) Prove that the set Z/nZ has n elements. (b) Find a minimal set of representatives for these n elements. (c) Prove that the operation gives a well-defined addition on Z/nZ Hint: The operution should not depend on the choice of coset representatives Verify that this gives Z/n2 the structure of an ahelian group. Be sure to verify all...
n=7 Question 3 3 pts Find the Fourier Sine series for the function defined by f(x) = { 0, 2n, 0 <*n n<<2n and write down, 1. The period T and the frequency wo of the Fourier Sine series 2. The coefficients for r = 1,2,3,...
In the following exercises, find the value(s) of k that makes each function continuous over the given interval. 145. f(x) = $3x + 2, x<k 12x – 3, k < x < 8 3 153. Apply the IVT to determine whether 2* = x has a solution in one of the intervals [1.25, 1.375] or [1.375, 1.5]. Briefly explain your response for each interval. Determine whether each of the given statements is true. Justify your response with explanation or counterexample....
Question 3 (1 point) The function f is defined by the power series 1)2 3! 5! 72n+1)! 1)% n-0 (2n+1) ! for all real numbers x. Use the first and second derivative test by finding f(x) and f"(x). Determine whether f has a local maximum, a local minimum, or neither at x=0. Give a reason for your answer. Use the Question 3 (1 point) The function f is defined by the power series 1)2 3! 5! 72n+1)! 1)% n-0 (2n+1)...
1. a) Let f(n) = 6n2 - 100n + 44 and g(n) = 0.5n3 . Prove that f(n) = O(g(n)) using the definition of Big-O notation. (You need to find constants c and n0). b) Let f(n) = 3n2 + n and g(n) = 2n2 . Use the definition of big-O notation to prove that f(n) = O(g(n)) (you need to find constants c and n0) and g(n) = O(f(n)) (you need to find constants c and n0). Conclude that...