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Say whether the following statements are true or false (T/F) and prove your answers (using limits). (i) 6n³/(log n + 1) = (n³) (ii) (iii) (T/F) 1000m² +10n log n + 100n +9999 = O(n²) (T/F) (T/F) log₂ n (2²)

Say whether the following statements are true or false (T/F) and prove your answers (using limits). (i) 6n³/(log n + 1) = (n³) (ii) (iii) (T/F) 1000m² +10n log n + 100n +9999 = O(n²) (T/F) (T/F) log₂ n (2²)

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Say whether the following statements are true or false (T/F) and prove your answers (using limits). (T/F) 1000n² + 10n log n + 100n +9999 = O(n²) (T/F) 5 log₂n = 0(2) (T/F) (i) 6n³/(logn+ 1) = 0 (n³) (ii)
Transcribed Image Text:Say whether the following statements are true or false (T/F) and prove your answers (using limits). (T/F) 1000n² + 10n log n + 100n +9999 = O(n²) (T/F) 5 log₂n = 0(2) (T/F) (i) 6n³/(logn+ 1) = 0 (n³) (ii)
Expert Solution
Step 1

i. 

When we divide 6n3 by logn then in average case it will return theta (n3) .

So It is True.

 

(ii).

It has n2 is the maximum variable so In worst case It will return O(n2).

So it is True.

 

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