In each of the following situations, indicate whether f = O (g), or f = (g), or both (in which case f = (g)). f (n) g (n) (a) n - 100 n - 200 (b) n1/2 n2/3 (c) 100n + log n n + (log n) 2 (d) nlog n 10nlog 10n (e) log 2n log 3n (f) 10 log n log (n2) (g) n1.01 nlog2 n (h) n2 / log n n (log n) 2 (i) n0.1 (log n) 10 (j) (log n) log n n / log n (k) √n (log n) 3 (l) n1/2 5log2 n (m) n2n 3n

Question

Mathematics

Markus Thornton

16 April, 10:19

In each of the following situations, indicate whether f = O (g), or f = (g), or both (in which case f = (g)). f (n) g (n) (a) n - 100 n - 200 (b) n1/2 n2/3 (c) 100n + log n n + (log n) 2 (d) nlog n 10nlog 10n (e) log 2n log 3n (f) 10 log n log (n2) (g) n1.01 nlog2 n (h) n2 / log n n (log n) 2 (i) n0.1 (log n) 10 (j) (log n) log n n / log n (k) √n (log n) 3 (l) n1/2 5log2 n (m) n2n 3n

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Answers (1)

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Stanley Hatfield · Answer 1

Check the explanation

Step-by-step explanation:

a)

f (n) = theta (g (n))

b) f=O (g)

c)

f (n) = theta (g (n))

d)

f (n) = theta (g (n))

e)

f (n) = theta (g (n))

f)

f (n) = theta (g (n))

g) f=omega (g)

h) f=omega (g)

i) f=omega (g)

j) f=omega (g)

k) f=omega (g)

l) f=O (g)

m) f=O (g)

n) f=theta (g)

o) f=omega (g)

p) f=O (g)

q) f=theta (g)