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(c) For each of the following f(n), show that f(n) is (g(n)) for the correct function g(n). Prove your result using the definitions from class, justifying your statement is true for all n 2 k. (provide the value of k). f(n)=√n(logn)² + + √nlogn + √n log n log n f(n)=2" n+100-4"-n log n-nº

(c) For each of the following f(n), show that f(n) is (g(n)) for the correct function g(n). Prove your result using the definitions from class, justifying your statement is true for all n 2 k. (provide the value of k). f(n)=√n(logn)² + + √nlogn + √n log n log n f(n)=2" n+100-4"-n log n-nº

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question 1: Asymptotic Notation (a) Rank the following functions in order (non-decresasing) of their asymptotic growth. Next to each function, write its big-Theta value, (ie. write the correct (g(n)) next to each function but you are not required to prove the big-Theta value). √n³(log n) +n (2¹0+6) log(n³), n(log n)² + n²+ n² logn 22+1, 5 (logn), 4/²+1, n² + log n (log 2")" 4+3″ (log n) + 2 n² + n (logn+n) 2logn+3, n (b) Determine if each of the following statements are true or false. If the statement is false, provide a counter example. If the statement is true, justify the statement using definitions from class. 1. If f(n) is O(n(logn)), does this imply that f(n) is also O(n²)? 2. If f(n) is O(n³), does this imply that f(n) is also O(2")? 3. If f(n) is O(n³), does this imply that f(n) is also f(n)? 4. If f(n) is (2"), does this imply that f(n) is also f(log n)? • f(n) = √n(logn)² + + √nlogn+√n logn f(n)=2" n+100-4"-n5 - n³ log n - n (2+3)(3+4"). (c) For each of the following f(n), show that f(n) is e(g(n)) for the correct function g(n). Prove your result using the definitions from class, justifying your statement is true for all n > k. (provide the value of k).
Transcribed Image Text:Question 1: Asymptotic Notation (a) Rank the following functions in order (non-decresasing) of their asymptotic growth. Next to each function, write its big-Theta value, (ie. write the correct (g(n)) next to each function but you are not required to prove the big-Theta value). √n³(log n) +n (2¹0+6) log(n³), n(log n)² + n²+ n² logn 22+1, 5 (logn), 4/²+1, n² + log n (log 2")" 4+3″ (log n) + 2 n² + n (logn+n) 2logn+3, n (b) Determine if each of the following statements are true or false. If the statement is false, provide a counter example. If the statement is true, justify the statement using definitions from class. 1. If f(n) is O(n(logn)), does this imply that f(n) is also O(n²)? 2. If f(n) is O(n³), does this imply that f(n) is also O(2")? 3. If f(n) is O(n³), does this imply that f(n) is also f(n)? 4. If f(n) is (2"), does this imply that f(n) is also f(log n)? • f(n) = √n(logn)² + + √nlogn+√n logn f(n)=2" n+100-4"-n5 - n³ log n - n (2+3)(3+4"). (c) For each of the following f(n), show that f(n) is e(g(n)) for the correct function g(n). Prove your result using the definitions from class, justifying your statement is true for all n > k. (provide the value of k).
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