Show that either g(n) = O(f(n)) or f(n) = O(g(n)) :
1. g(n) = n^2 +7n , f(n) = ^3 -2n^2
2. g(n) = 2n +4 , f(n) = 6lg(n^2)
Show that either g(n) = O(f(n)) or f(n) = O(g(n)) : 1. g(n) = n^2 +7n...
2. (10 pts.) Show that either g(n) Ofn)) or frn) -O(g(n) for the following. g(n)n2 + 7 n, f(n)-ns_2㎡ a. b. g(n)= 2n + 4,f(n)=61g(n*)
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: ???? ? = ???? ?)???? ?...
Which of the following series diverges? n +2 2n -1 n1 n+3 O A. 2 B. O C. 1,3 O D. 1, 2 OE. 2, 3 F. None O G. O H. 1,2,3 Find the sum of the series A. B. OC. 1/10 D. 1/2 3/2 3/4 OE. 1 F. 5/12 OG. 1/4 H. Divergent Which of the following series converges? oo 2n 1.Σ n 1 23n nE1 (n+ 1)3 n+ 1 3. O A. None O B. 2 O...
Asymptotic notation O satisfies the transitive property i.e. if f(n)=O(g(n)) and g(n)=O(h(n)), then f(n)=O(h(n)). Now we know that 2n =O(2n-1), 2n-1 =O(2n-2?),....... , 2i=O(2i-1?),....... So using rule of transitivity, we can write 2n =O(2i-1?).We can go extending this, so that finally 2n =O(2k?), where k is constant.So we can write 2n =O(1?). Do you agree to what has been proved?If not,where is the fallacy? 6 marks (ALGORITHM ANALYSIS AND DESIGN based problem)
7n Use Mathematical Induction to prove that Σ 2-2n+1-2, for all n e N
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...
Perform the indicated operation g(n)=2n-2 f(n)=n^2+1 FIND g(n)+f(n)
1. h(a) = -a2-a g(a) = 2a+1 Find (h-g)(-4) 2. f(n) = 2n +4 g(n) = 3n-1 Find (f+g)(-3)
For f(n) = 1000 · 2" and g(n) = 3" we have: g(n) = O(f(n)) O g(n) =(f(n)) O g(n) = 2(f(n))
Question2: 1. f(n)-O(g(n) if there exist c, no>0 such that f(n)for all n 2 no- 2. f(n)-2(g(n)) if there existc, no>0 such that f(n)for all n 2 no- 3. f(n)- (g(n)) if there exist C1, C2,no > 0 such that-for all n 2 no-