Relative asymptotic growths
Indicate, for each pair of expressions (A, B) in the table below, whether A is O, o, Ω, ω, or Θ of B. Assume that k ≥ 1, ∈ > 0, and c > 1 are constants. Your answer should be in the form of the table with “yes” or “no” written in each box.
| A | B | O | o | Ω | ω | Θ |
a. | lgk n | n∈ |
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b. | nk | cn |
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c. | nsin n |
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d. | 2n | 2n/2 |
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e. | nlgc | clgn |
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f. | lg(n!) | lg(nn) |
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