Asymptotic function relationships. Verify each of the following statements by the definitions to see if they are true or false 1. If ?(?) = Θ(?), then ??(?) = Θ(?2 ) 2. If ?(?) = ?(?2 ) and ?(?) = Ω(?(?)), then ?(?) = ?(?2) 3. If ?(?) = ?(0. 5?2 ) and ?(?) = Ω(7?2 + ?????), then ?(?) = Θ(?2 ) 4. If ?(?) = ?(?3 ), then ?(?) = Ω(2?3 ) 5. If ?(?) = Θ(?3 ), then ?(?) = ?(2n )

C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter6: User-defined Functions
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Asymptotic function relationships. Verify each of the following statements by the definitions to see if they are true or false

1. If ?(?) = Θ(?), then ??(?) = Θ(?2 )

2. If ?(?) = ?(?2 ) and ?(?) = Ω(?(?)), then ?(?) = ?(?2)

3. If ?(?) = ?(0. 5?2 ) and ?(?) = Ω(7?2 + ?????), then ?(?) = Θ(?2 )

4. If ?(?) = ?(?3 ), then ?(?) = Ω(2?3 )

5. If ?(?) = Θ(?3 ), then ?(?) = ?(2n )

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