Question

1. (16 Points) True or false. (a) $5n^2 = O(n^3)$ (b) $n^2 + 10n = O(n^3)$ (c) $3n + 1 = O(n)$ (d) $5n^2 = \Omega(n^2)$ (e) $n = O(5n^2)$ (f) $6n^2 + n = \Omega(n^3)$ (g) $a^n = O(b^n)$, $b > a > 1$ (h) $lg\ n = O(n)$ Hint: f(n) = O(g(n)) Asymptotically, f(n) "?" g(n) f(n) = \Omega(g(n)) Asymptotically, f(n) "?" g(n) f(n) = \Theta(g(n)) Asymptotically, f(n) "=" g(n)

          1. (16 Points) True or false.
(a) $5n^2 = O(n^3)$
(b) $n^2 + 10n = O(n^3)$
(c) $3n + 1 = O(n)$
(d) $5n^2 = \Omega(n^2)$
(e) $n = O(5n^2)$
(f) $6n^2 + n = \Omega(n^3)$
(g) $a^n = O(b^n)$, $b > a > 1$
(h) $lg\ n = O(n)$
Hint:
f(n) = O(g(n))
Asymptotically, f(n) "?" g(n)
f(n) = \Omega(g(n))
Asymptotically, f(n) "?" g(n)
f(n) = \Theta(g(n))
Asymptotically, f(n) "=" g(n)

1. (16 Points) True or false.
(a) 5n^2 = O(n^3)
(b) n^2 + 10n = O(n^3)
(c) 3n + 1 = O(n)
(d) 5n^2 = Ω(n^2)
(e) n = O(5n^2)
(f) 6n^2 + n = Ω(n^3)
(g) a^n = O(b^n), b > a > 1
(h) lg n = O(n)
Hint:
f(n) = O(g(n))
Asymptotically, f(n) "?" g(n)
f(n) = Ω(g(n))
Asymptotically, f(n) "?" g(n)
f(n) = Θ(g(n))
Asymptotically, f(n) "=" g(n)

Added by Irene G.

Intermediate Algebra

Julie Miller, Molly O'Neill, Nancy Hyde 5th Edition

Chapter 10

Instant Answer

Solved by Expert Maryam Riaz

Step 1

5n is a constant multiple of n, so it is O(n). Show more…

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1.16 Points) True or false. 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1 (a) 5n = O(n) (b) n + 10n = O(n) (c) 3n + 1 = O(n) (d) 5n = n (e) n = O(5n) (f) 6n + n = n (g) a = O(b), b > a > 1 (h) n = O(n) Hint: f(n) = O(g(n)) Asymptotically, f(n) = Î˜(g(n)) Asymptotically, f(n) = O(g(n)) Asymptotically, f(n) = Î©(g(n)) 21 n^2 nlogn n logn 1 : 4 2 3 6 5 7 8