Blank #1: f(n) <= cg(n) Blank #2: f(n) >= cg(n) Blank #3: c1g(n) <= f(n) <= c2g(n)
Question2: 1. f(n)-O(g(n) if there exist c, no>0 such that f(n)for all n 2 no- 2....
(a) Consider the following C++ function: 1 int g(int n) { 2 if (n == 0) return 0; 3 return (n-1 + g(n-1)); 4} (b) Consider the following C++ function: 1 bool Function (const vector <int >& a) { 2 for (int i = 0; i < a. size ()-1; i ++) { 3 for (int j = i +1; j < a. size (); j ++) { 4 if (a[i] == a[j]) return false; 5 6 } 7 return...
(1) Suppose f :(M, d) + (N,0) is not uniformly continuous. Show that there exist an a > 0 and sequences (Xn) and (yn) in M such that d(Ion, yn) < and o(f(xn), f(n)) > € VnE N. (Hint: Negation of the definition of uniform continuity.)
Formal Definitions of Big-Oh, Big-Theta and Big-Omega:
1. Use the formal definition of Big-Oh to prove that if f(n) is a decreasing function, then f(n) = 0(1). A decreasing function is one in which f(x1) f(r2) if and only if xi 5 r2. You may assume that f(n) is positive evervwhere Hint: drawing a picture might make the proof for this problem more obvious 2. Use the formal definition of Big-Oh to prove that if f(n) = 0(g(n)) and g(n)...
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)
For which of the following functions does lim 2->0 (2) exist? -1, x < 0 1. f(x) = { 0, x=0 (1,2 > 0 2. f(x) = {1x1, x 70 (1,2 = 0 sin(x) 3. f(x) = { (1, x = 0 2,270 1 only 3 only 1 and 3 only 2 and 3 only 2 only
5. Methanol gas combustion is represented with the following reaction 2 H3C-O-H(g) + 3 0=0(g) 20=C=O(g) + 4H-O-H(g) Calculate the AH x using the average bond dissociation energies from the table below, for 1 mole of methanol. Bond Energy kJ/mol Bond Energy kJ/mol Bond Energy kJ/mol Bond Bond 436 347 414 611 389 Bond C-C Сс Cc C-N CEN C-o H-H HC H- N H-O HS HF H-C1 HBr H- 837 305 615 891 8 565 163 418 946 222...
Problem 2. Let C[0, 1] be the set of all continuous functions from [0, 1] to R. For any f, g є Cl0, 11 define - max f(x) - g(z) and di(f,g)-If(x) - g(x)d. a) Prove that for any n 2 1, one can find n points in C[O, 1 such that, in daup metric, the distance between any two points is equai to 1. b) Can one find 100 points in C[0, 1] such that, in di metric, the...
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))
1. Prove that the proposition P(0) is true, where P(n) is “if n > 1, then n? > n" and the domain consists of all integers
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