A. Prove the following: 1. n(n – 1) = 0(n²) 2. 10 log, n+ 4 = ®(log, n) 3. 3n + 5 = 0(n²) 4. 100n = 0(n) 5. n? + 10n + 1 = N(n²) 6. 100n? + n + 10 = N(n²)

Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
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Chapter1: Computer Networks And The Internet
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DASTRAL EXERCISE 3 ALGORITHMIC ANALYSIS

ALGORITHM ANALYSIS
General Instructions:
PROBLEM SOLVING: ASYMPTOTIC NOTATIONS.
A. Prove the following:
1. n(n – 1) = 0(n²)
2. 10 log, n+ 4 = 0(log, n)
3. 3n + 5 = 0(n²)
4. 100n =
O(n)
5. n? + 10n + 1 = 0(n?)
6. 100n? +n + 10 = N(n?)
Transcribed Image Text:ALGORITHM ANALYSIS General Instructions: PROBLEM SOLVING: ASYMPTOTIC NOTATIONS. A. Prove the following: 1. n(n – 1) = 0(n²) 2. 10 log, n+ 4 = 0(log, n) 3. 3n + 5 = 0(n²) 4. 100n = O(n) 5. n? + 10n + 1 = 0(n?) 6. 100n? +n + 10 = N(n?)
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