--> In big-oh notation the term with highest degree dominates the order of the function.
f1 = 3n2 - 5n + 6
f2 = 5n2 + 2n - 1
We can write f1 = O(f2) and f2 = O(f1)
--> Similarly we can give following example for f3 and f4
f3 = 2n + 5n2
f4 = 2n - 6n2
We can write f3 = O(f4) and f4 = O(f3)
[ 6 marks] Give examples of two pairs of functions f1-f and fz-f such that each...
1. Asymptotic Bounds la) Rank the following functions at ascending order; that is, find an arrangement fi, f2,..., fg of the functions satisfying f1 = O(f2), fz = O(fz), ...,f7= O(fy). Briefly show your work for this problem. (2pts) Ign n n n? (lg n) len 21gn n? +n nlgign 1b) Partition your list into equivalence classes such that f(n) and g(n) are in the same class if and only if f(n) = (g(n)). (2pts)
Let f1 and f2 be asymptotically positive non-decreasing functions. Prove or disprove each of the following conjectures. To disprove, give a counterexample. a.If f1(n) = Theta(g(n)) and f2(n) = Theta(g(n)) then f1(n) + f2(n) = Theta(g(n)) b.If f1(n) = O(g(n)) and f2(n) = O(g(n))then f1(n) = O(f2(n))
(a) State what is meant by saying that F is a σ-field on a set Ω. I. (b) Let F1 and F2 be two-fields on a set Ω. Is Ћ UF2 a-field on Ω? If yes, show that Fİ UF2 is a σ-field on Ω. If not, give a counterexample. , isaơ-field on . (c) Let 2-11,2,3,4,5,6,7,8,9,10) and F(A) be the o-field generated by A - 11,2,3,5, 10), 2,8,51, 16,7)1 (i) Find F(A); (ii) Give an example of four-fields F1,...
1. (10 pts) For each of the following pairs of functions, indicate whether f = 0(g), f = Ω(g), or both (in which case f-6(1). You do not need to explain your answer. f(n) (n) a) n (b) n-1n+1 (c) 1000n 0.01n2 (d) 10n2 n (lg n)2 21 е) n (f) 3" (g) 4" rl. 72 i-0 2. (12 pts) Sort the following functions by increasing order of growth. For every pair of consecutive functions f(n) and g(n) in the...
Consider the following definition of equivalent sets of functional dependencies on a relation: “Two sets of functional dependencies F and F’ on a relation R are equivalent if all FD’s in F’ follow from the ones in F, and all the FD’s in F follow from the ones in F’.” Given a relation R(A, B, C) with the following sets of functional dependencies: F1 = {A B, B C}, F2 = {A B, A C}, and...
For each pair of functions f(n) and g(n), indicate whether f(n) = O(g(n)), f(n) = Ω(g(n)), and/or f(n) = Θ(g(n)), and provide a brief explanation of your reasoning. (Your explanation can be the same for all three; for example, “the two functions differ by only a multiplicative constant” could justify why f(n) = n, g(n) = 2n are related by big-O, big-Omega, and big-Theta.) i. f(n) = n^2 log n, g(n) = 100n^2 ii. f(n) = 100, g(n) = log(log(log...
2. What are the two primary functions of a league? Give examples of each. From an economic standpoint what does a league structure do to the market power of the owners?
*9. For each of the following pairs of functions, determine the highest order of contact between the two functions at the indicated point xo: (e) f,g : R-R given by f(x)and g(x) 1+2r ro0 (f) f, g : (0, oo) → R given by f(r) = In(2) and g(z) = (z-1)3 + In(z): zo = 1. (g) f.g: (0, oo) -R given by f(x)-In(x) and g(x)-(x 1)200 +ln(x); ro 1 x-1)200 *9. For each of the following pairs of functions,...
Problem 3 (3 marks) 708.335.10-12 F/m, u = 1.25663706.10-6 H/m). A uniform plane wave propagates in seawater (o = 4 S/m, e = Page 1/2 frequencies: fi = 10 GHz and f2 = 100 kHz. (2.5 a) Find the propagation constant y, a and ß at two mark) b) If you were to send a signal in seawater, which frequency would you choose? Why? (0.5 mark) Problem 3 (3 marks) 708.335.10-12 F/m, u = 1.25663706.10-6 H/m). A uniform plane wave...