Question 4: True Question 5: False
QUESTION 4 Tell whether the following function is O(NZ): f(N) = N * log(N) O True...
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
HW10.6) If f(z) nz", what function is expressed by the power series n-O 1 n-0
HW10.6) If f(z) nz", what function is expressed by the power series n-O 1 n-0
Which of the following could be false? A. n2/(log(n)) = O(n2). B. (log n)1000 = O(n1//1000). C. 1/n = O(1/(log(n))). D. 2(log(n))^2 = O(n2). E. None of the above.
Compare the following pairs of functions f, g. In each case, say whether f- o(g) f-w(g), or f = Θ(g), and prove your claim. 157. f(n) -100n+logn, gn) (logn)2. 158,介f(n) = logn, g(n) = log log(n2). 159. . f(n)-n2/log n, g(n) = n(log n)2. 160·介介f(n)-(log n)106.9(n)-n10-6 . 161. (n)logn, g(n) (log nlog n 162. f(n) n2, gn) 3.
Compare the following pairs of functions f, g. In each case, say whether f- o(g) f-w(g), or f = Θ(g), and prove...
4. Determine whether or not the following are true and provide a full derivation explaining your answer for each. The domain of the functions of n below is the positive real numbers. For convenience, you may assume that the logs are in the base of your choice, but you should specify what base you are using in your derivation. 510g(n+is O(n) d. +3 log(log(n))+ Slozat)+ is o 5log(n+1) e. log(n3 n-3) is 0(n2)
4. Determine whether or not the following...
1) True or false? a. n2 = O(n3) b. 2n2 + 1 = O(n2) c. n1/2 = O(log n) d. log n = O(n1/2 ) e. log n + n1/2 = O(n2) f. log n = O( n-1/2) g. log n = O( 1/n ) h. log (n + 3) = q(n1/2) i. n + n1/2= W( n2 - n )
Here are some common orders of growth, ranked from no growth to
fastest growth:
Θ(1) — constant time takes the same amount of time regardless
of input size
Θ(log n) — logarithmic time
Θ(n) — linear time
Θ(n log n) — linearithmic time
Θ(n2 ) — quadratic time
Θ(n3 ), etc. — polynomial time
Θ(2n), Θ(3n), etc. — exponential time
(considered “intractable”; these are really, really horrible)
In addition, some programs will never terminate if they get
stuck in an...
nlog(n) = O(nlog(log(n)) True or False and explain why
QUESTION 1 (x + x2)log x + x2.5 is ou O x2 log x O X3 O x2 O x log x QUESTION 2 If f(x) is O(g(x)) and g(x) is O(h(x)) then f(x) is O(h(x)). True False
Use the graph below to determine whether the statements about the function y=f(x) are true or false. Ay 10- 8- 6 -10 -8 -6 -4 -2 2 8 10 True or false; lim f(x)= 9. X-3+ O True O False True or false: lim f(x) = 3. X-0- O True O False True or false: lim f(x) = lim f(x). X-0 X0- O True False True or false: lim f(x) exists. x0 0 True 0 False True or false: lim...