ONLY THE LAST ONE (4) . DISCRETE MATH
ONLY THE LAST ONE (4) . DISCRETE MATH Problem 1: Show that f(n) = (n +...
Discrete Math Use mathematical induction to prove that for all positive integers n, 2 + 4 + ... + (2n) = n(n+1).
3. (10 pts) For each of the following functions f(n), prove the stated claim by providing constants no C1, and c2 such that for all n2 no, cig(n) S f(n) or f(n) c2g(n), and provide a calculation that shows that this inequality does indeed hold (a) f(n) 2n2 3n3-50nlgn10 0(n3) O(g(n)) (b) f(n)-2n log n + 3n2-10n-10-Ω ( 2)-0(g(n))
Discrete Math □ Prove or disprove: If n is any odd integer then (-1)"--1 Problem 6:
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...
Please solve Q1, this is a discrete math question. "O" represents Oh notation, f=O(g) if there are positive constants c and n0 such that for any n≥ n0, f(n) ≤ c·g(n). Please include all your explanations. Problem 1 (3 points) Find the least integer t such that (n° + n2 log(n)) (log(n) + 1) + (8 log(n) +6) (n3 + 4) is 0 (nt). Briefly justify your answer (i.e., why it is o (nt) and why it is not 0...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci number. By definition Fibonnaci(0) is 1, Fibonnaci(1) is 1, Fibonnaci(2) is 2, Fibonnaci(3) is 3, Fibonnaci(4) is 5, and so on. Your function may only use a constant amount of memory (i.e. no auxiliary array). Argue that the running time of the function is Θ(n), i.e. the function is linear in n. 2. (10 points) Order the following functions by growth rate: N, \N,...
please.show work and answer full.question. this js discrete math. 1. Determine whether each of the functions is one-to-one and/or onto. a. f:R - R, f(x) = 19(x) = log2(x) one-to-one onto onto one-to-one b. f:N NX N, f(x) = (x,x) onto one-to-one c. f:R+ (-1,1), f(x) = cos(x) one-to-one onto d. 8:[2,3) –> (0, +), f(x) = ***
discrete math problem 2) X+1 Show that the function g is one-to- If g:(2,) - (2,) is defined by 9(x) = one and onto. X- 2
Discrete Math: Divisibility (Need Help ASAP, will upvote) 1) Prove that if n is an odd positive integer, then n^2 is congruent to 1 (mod 8)
Discrete math show all work please Use mathematical induction to prove that the statements are true for every positive integer n. n[xn - (x - 2)] 1 + [x2 - (x - 1)] + [x:3 - (x - 1)] + ... + x n - (x - 1)] = 2 where x is any integer = 1