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7.a) Rank the following time bounds. That is write them as f₁, f2, ..., f6 and show that fi = O(fi+1) for all 1 ≤ i ≤5 (You may use limit lemma theorem) • 3nª + 6n n log(n¹000) • 7n³ log(n) + 1000 • 3n ● ● 6 • 1024m² + 4n + 460 7b.) Prove that k(n)= n²+3n is (n²).

7.a) Rank the following time bounds. That is write them as f₁, f2, ..., f6 and show that fi = O(fi+1) for all 1 ≤ i ≤5 (You may use limit lemma theorem) • 3nª + 6n n log(n¹000) • 7n³ log(n) + 1000 • 3n ● ● 6 • 1024m² + 4n + 460 7b.) Prove that k(n)= n²+3n is (n²).

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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7.a) Rank the following time bounds. That is write them as f1, f2, ..., f6 and show that fi = O(fi+1) for all 1 ≤ i ≤5 (You may use limit lemma theorem) • 3n¹ + 6n ● n log(n¹000) 7n³ log(n) + 1000 • 3n .6 · 1024n² + 4n + 460 7b.) Prove that k(n) = n² +3n is N(n²).
Transcribed Image Text:7.a) Rank the following time bounds. That is write them as f1, f2, ..., f6 and show that fi = O(fi+1) for all 1 ≤ i ≤5 (You may use limit lemma theorem) • 3n¹ + 6n ● n log(n¹000) 7n³ log(n) + 1000 • 3n .6 · 1024n² + 4n + 460 7b.) Prove that k(n) = n² +3n is N(n²).
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