6 23 99 1 Find a simple g(n) such that f(n) -e(g(n)), by proving that f(n) - O(g(n)), and that f(n)- S(g(n). Don't...
please answer these three questions thank you! (e) Given that f(n) € O(n) and g(n) e O(n log n), please formally prove that f(n) + g(n) € O(nº). [4 (6) We know that kn is in O(n) for any constant k. Is the following claim correct? Briefly explain. I kn = ŻO(n) = O(n?) 13 o f is a function that satisfies the following: • f is in O(n), . f is in 2(1), • f is neither in e(1)...
Let f(n) = 5n^2. Prove that f(n) = O(n^3). Let f(n) = 7n^2. Prove that f(n) = Ω(n). Let f(n) = 3n. Prove that f(n) =ꙍ (√n). Let f(n) = 3n+2. Prove that f(n) = Θ (n). Let k > 0 and c > 0 be any positive constants. Prove that (n + k)c = O(nc). Prove that lg(n!) = O(n lg n). Let g(n) = log10(n). Prove that g(n) = Θ(lg n). (hint: ???? ? = ???? ?)???? ?...
Problem 3's picture are given below. 5. (a) Let G = (V, E) be a weighted connected undirected simple graph. For n 1, let cycles in G. Modify {e1, e2,.. . ,en} be a subset of edges (from E) that includes no Kruskal's algorithm in order to obtain a spanning tree of G that is minimal among all the spanning trees of G that include the edges e1, e2, . . . , Cn. (b) Apply your algorithm in (a)...
1. Use mathematical induction to prove ZM-1), in Ik + 6 for integers n and k where 1 <k<n - 1. = 2. Show that I" - P(m + k,m) = P(m+n,m+1) (m + 1) F. (You may use any of the formulas (1) through (14”).)
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...
1. Given n=2500 and p=0.86, find the margin of error E that corresponds to a 99% confidence level 2. you are given a margin of error as three percentage points in a confidence level of 99%. If the same percentage from arecent poll is 35%, find the minimum sample size to estimate a population proportion. corresponds to a 99% confidence (1 point) 1. Given n level. 2500 and β-086, find the margin of error E that 0.014 0.048 0.018 0...
10. Let S be a regular surface with E = G = (1 + u2 + U2)2, F = 0 and e = 2=-g,f=0. (a) Find the Gaussian and mean curvatures b)Find the principal curvatures and directions of S 10. Let S be a regular surface with E = G = (1 + u2 + U2)2, F = 0 and e = 2=-g,f=0. (a) Find the Gaussian and mean curvatures b)Find the principal curvatures and directions of S
a graph theory homework questions parts c,d,e,f 6. Let G be the fllowing graph: 1) Fig, 7.7.1 (n) Does G have a perfect matching? (b) Find four maximum matchings in G. (c) Is there any maximum matching in G that contains the edge cl? (d) Find four maximal matchings (for definition, see Problem 7.6.20) that are not maximum. (e) Find in G (1) a maximum independent set, (ii) a minimum v-cover, and iii) n minimum c-cover. (f) Find the values...
E(s) In the figure below, find the transfer function G(s) = N(s) N(s) Y(s) 10 E(s) R(s) s+2 s(s + 1) 0.5s E(s) In the figure below, find the transfer function G(s) = N(s) N(s) Y(s) 10 E(s) R(s) s+2 s(s + 1) 0.5s
2. (6 points) Let f(n) = 2n3 and g(n) = vm+1. Find (fog)(n) and (g-n(n).