4.7 - Lower Bounds and Θ Notation

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Big-Theta notation (Θ) defines an equivalence relation on the set of functions.

True

Determine the proper relationship between the following pair of functions. f(n) = 2^n, g(n) = 3^n

f(n)is O(g(n))

Determine the proper relationship between the following pair of functions. f(n) = 2^n, g(n) = n^n

f(n)is O(g(n))

Determine the proper relationship between the following pair of functions. f(n) = √n, g(n) = log (n^2)

f(n)is Ω(g(n))

The Sequential Search algorithm is Θ(n^2).

False

The Sequential Search algorithm is Θ(n^n).

False

Determine the proper relationship between the following pair of functions. f(n) = 2^n, g(n) = 10n^2

f(n)is Ω(g(n))

Determine the proper relationship between the following pair of functions. f(n) = 2^n, g(n) = n log n

f(n)is Ω(g(n))

Determine the proper relationship between the following pair of functions. f(n) = log^2 n, g(n) = logn

f(n)is Ω(g(n))

Determine the proper relationship between the following pair of functions. f(n) = n. g(n) = log^2 n

f(n)is Ω(g(n))

Determine the proper relationship between the following pair of functions. f(n) = nlogn + n, g(n) = logn

f(n)is Ω(g(n))

For what value of k is √n = Θ(n^k)?

0.5

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