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Determine the 'Big Oh' for the following 8n³ +4n² +log n¹ +4".

Determine the 'Big Oh' for the following 8n³ +4n² +log n¹ +4".

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Determine the 'Big Oh' for the following 8n³ +4n² +log n¹ +4".
Transcribed Image Text:Determine the 'Big Oh' for the following 8n³ +4n² +log n¹ +4".
Expert Solution
Step 1

We know, 8n3 = O(n3) 

      4n2 < 4n3 for all n > 1 => 4n2 = O(n3) 

      log n4 = 4log n < 4n3 for all n ≥ 1

      => log n4 = O(n3) 

 

Now, we see, n3 < 4n for any n ≥ 1

    => n3 = O(4n) 

 

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