n2 = O(7n2 + 3logn + 22) is correct since nighest power of n is same in LHS and RHS
2n = O(n3 +3n2 + 7logn + 2) is not true since highesest power of LHS is 2n bt of RHS is n2
5n + 3logn + 1 = O(nlogn) is also not true ssince highest power of n is 1 in LHS, and in RHS its nlogn and are not equal
7nlogn + 3n = O(11n + 5logn + 7) you can see that on ih RHS it is n + logn which is not equal to nlogn in left
2n2+3nlogn+7n+4logn + 1 = O(2n + 3n + 7) is again false since LHS has highest power n2 and of RHS it is 2n
Given the following statements, mark those correct statements as True and mark those incorrect statements as...
Prove or disprove the following statements, using the relationship among typical growth-rate functions seen in class. a)n^15log n + n^9 is O(n^9 log n) b) 15^7n^5 + 5n^4 + 8000000n^2 + n is Θ(n^3) c) n^n is Ω (n!) d) 0.01n^9 + 800000n^7 is O(n^9) e) n^14 + 0.0000001n^5 is Ω(n^13) f) n! is O(3n)
Determine whether each of the following statements is true or false. In each case, answer true or false, and justify your answer. 3n^2 - 42 = O(n^2) n^2 = O(n log n) 1/n = O(1) n^n = ohm(2^n)
(6 pts) Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges Vn (n + 1)(22-1)" 2n 4 7n +4 sin(3n)
(6 pts) Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges Vn (n + 1)(22-1)" 2n 4 7n +4 sin(3n)
O(log(log(N))) < O(log(N)) a. True b. False O(N ) < O(log(N)) a. True b. False O( N5) < O(N2 - 3N + 2) a. True b. False O(2N) < O(N2) a. True b. False
Use the definition of Θ in order to show the following: a. 5n^3 + 2n^2 + 3n = Θ (n^3) b. sqroot (7n^2 + 2n − 8) = Θ( ?)
Question 2 Part A (2 points): Select "True" or "False" and correct false statements and mark your answers in the talte ast page: 1. When developing feasible alternatives, the "nominal group technique" aims at incorporating individual ideas into a group consensus. It also removes the undesirable effect of classical brainstorming. True False 2. For solutions to engineering problems to be economically acceptable, the long-term benefits of these solutions must be equal or more than their long-term costs, among other things....
1. Give an asymptotically tight bound to each of the following expressions: 3n^2 + 2n^3 3n log n + 2n^2 2^n + 3^n 2. Arrange the following asymptotic family from lower order to higher order. The first has been done for you. O(n log n) O(n^3) O(log n) O(n^2 log n) O(n) O(3^n) O(2^n) 3. At work, Peter needs to solve a problem of different sizes. He has two algorithms available to solve the problem. Algorithm A can solve the...
5. 5 Let f(x) be continuous and differentiable on f(5) = 4. Mark TRUE or FALSE for the following statements and JUSTIFY. (No points will be given without the correct justification) [0, 10] with f(0) = f(10) 0 and (E) There is some c E (0,5) such that f'(c) =
5. 5 Let f(x) be continuous and differentiable on f(5) = 4. Mark TRUE or FALSE for the following statements and JUSTIFY. (No points will be given without the correct...
(1 point) Each of the following statements is an attempt to show that a given series is convergent or divergent not using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (or "correct") if the argument is valid, or enterI (for "incorrect") if any part of the argument is flawed (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.) 1. For all n^ 1 arctan(n 2....
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark 1729 is O(1) b) 3 marks 2n2-4n -3 is O(n2) 2. [3 marks] Using the definition of Big-Oh, prove that 2n2(n 1) is not O(n2) 3. 6 marks Let f(n),g(n), h(n) be complexity functions. Using the definition of Big-Oh, prove the following two claims a) 3 marks Let k be a positive real constant and f(n) is O(g(n)), then k f(n) is O(g(n)) b)...