Homework Help is Here – Start Your Trial Now!
Engineering
Computer Engineering
Yihan recently learned the asymptotical analysis. The key idea is to evaluate the growth of a function. For example, she now knows that n² grows faster than n. She wants to know whether she really understands the idea, so she has created a little task. First of all, she found a lot of functions here: 91 3n log n² 92: n! log(n!) 93 n²+n 2n+1 94: n³ 96 97 911: √n 916 n 912 917 2n 913 918 nlogn 99 ln ln n 914 √log n 919 5n² 13n+6 log² n 910: 10000 915: log √n 920 n/log n Note: log n = log2 n; ln n = loge n; log²1 n = (log n)2; n! is the factorial of n, i.e., n! = 1 x 2 xxn. 95: 98 log log n (n + 1)! hen let's compare some them pairwise. a) b) c) Compare 912 log log n and 914 √logn. Which one grows faster? Please explain briefly. Compare 92: n! and 913: (n+1)!. Which one grows faster? Please explain briefly. Compare 920 n/logn and 911 √n. Which one grows faster? Please explain briefly. Yihan finds out that 912 log log n and 99: In ln n should be asymptotically equivalent (i.e.. log log n = (In ln n)). Can you prove this? d) :

Yihan recently learned the asymptotical analysis. The key idea is to evaluate the growth of a function. For example, she now knows that n² grows faster than n. She wants to know whether she really understands the idea, so she has created a little task. First of all, she found a lot of functions here: 91 3n log n² 92: n! log(n!) 93 n²+n 2n+1 94: n³ 96 97 911: √n 916 n 912 917 2n 913 918 nlogn 99 ln ln n 914 √log n 919 5n² 13n+6 log² n 910: 10000 915: log √n 920 n/log n Note: log n = log2 n; ln n = loge n; log²1 n = (log n)2; n! is the factorial of n, i.e., n! = 1 x 2 xxn. 95: 98 log log n (n + 1)! hen let's compare some them pairwise. a) b) c) Compare 912 log log n and 914 √logn. Which one grows faster? Please explain briefly. Compare 92: n! and 913: (n+1)!. Which one grows faster? Please explain briefly. Compare 920 n/logn and 911 √n. Which one grows faster? Please explain briefly. Yihan finds out that 912 log log n and 99: In ln n should be asymptotically equivalent (i.e.. log log n = (In ln n)). Can you prove this? d) :

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...
See similar textbooks
icon
Related questions
Question

Question has complete information. There is no missing informaito

Yihan recently learned the asymptotical analysis. The key idea is to evaluate the growth of a function. For example, she now knows that n² grows faster than n. She wants to know whether she really understands the idea, so she has created a little task. First of all, she found a lot of functions here: 91 32 96 log n² 916 n 97: log(n!) 911 √n 912 log logn 917 2n 98 2n+1 913 (n+1)! 918 nlogn 99 ln ln n √logn 919: 5n² - 13n + 6 914 915 log √n 910: 10000 Note: log n = log2 n; ln n = loge n; log² n = (log n)²; n! is the factorial of n, i.e., n! = 1 × 2 × ... xn. 920 n/log n 92: n! 93 n² + n 94 : n³ 95 log² n (4) Then let's compare some them pairwise. (a) (b) (c) Compare 912 log log n and 914: √logn. Which one grows faster? Please explain briefly. Compare 92n! and 913: (n + 1)!. Which one grows faster? Please explain briefly. Compare 920 n/logn and 911 √n. Which one grows faster? Please explain briefly. Yihan finds out that 912 log log n and g9 : In ln n should be asymptotically equivalent (i.e., log log n = (In In n)). Can you prove this? (d) :
Transcribed Image Text:Yihan recently learned the asymptotical analysis. The key idea is to evaluate the growth of a function. For example, she now knows that n² grows faster than n. She wants to know whether she really understands the idea, so she has created a little task. First of all, she found a lot of functions here: 91 32 96 log n² 916 n 97: log(n!) 911 √n 912 log logn 917 2n 98 2n+1 913 (n+1)! 918 nlogn 99 ln ln n √logn 919: 5n² - 13n + 6 914 915 log √n 910: 10000 Note: log n = log2 n; ln n = loge n; log² n = (log n)²; n! is the factorial of n, i.e., n! = 1 × 2 × ... xn. 920 n/log n 92: n! 93 n² + n 94 : n³ 95 log² n (4) Then let's compare some them pairwise. (a) (b) (c) Compare 912 log log n and 914: √logn. Which one grows faster? Please explain briefly. Compare 92n! and 913: (n + 1)!. Which one grows faster? Please explain briefly. Compare 920 n/logn and 911 √n. Which one grows faster? Please explain briefly. Yihan finds out that 912 log log n and g9 : In ln n should be asymptotically equivalent (i.e., log log n = (In In n)). Can you prove this? (d) :
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY
SEE MORE TEXTBOOKS