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For each of the following pairs of functions, either f(n) is O(g(n)), f(n) is (g(n)), or f(n) = Ⓒ(g(n)). Determine which relationship is correct. Show work. Note: You should use limits as shown in the slides from lecture. a) f(n) = log₂ (n³), g(n) = n³ log₂ n b) f(n) = 5¹, g(n) = 5n+3 c) f(n) = 4", g(n) = 9n d) f(n)= 27, g(n) = log₂ 2048

For each of the following pairs of functions, either f(n) is O(g(n)), f(n) is (g(n)), or f(n) = Ⓒ(g(n)). Determine which relationship is correct. Show work. Note: You should use limits as shown in the slides from lecture. a) f(n) = log₂ (n³), g(n) = n³ log₂ n b) f(n) = 5¹, g(n) = 5n+3 c) f(n) = 4", g(n) = 9n d) f(n)= 27, g(n) = log₂ 2048

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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1. For each of the following pairs of functions, either f(n) is O(g(n)), f(n) is N(g(n)), or f(n) = Ⓒ(g(n)). Determine which relationship is correct. Show work. Note: You should use limits as shown in the slides from lecture. a) f(n) = log₂ (n³), g(n) = n³ log₂ n b) f(n) = 5¹, g(n) = 5n+3 c) f(n) = 4¹, g(n) = 9n d) f(n) = 27, g(n) = log₂ 2048
Transcribed Image Text:1. For each of the following pairs of functions, either f(n) is O(g(n)), f(n) is N(g(n)), or f(n) = Ⓒ(g(n)). Determine which relationship is correct. Show work. Note: You should use limits as shown in the slides from lecture. a) f(n) = log₂ (n³), g(n) = n³ log₂ n b) f(n) = 5¹, g(n) = 5n+3 c) f(n) = 4¹, g(n) = 9n d) f(n) = 27, g(n) = log₂ 2048
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