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f(n) = n³, g(n) = 6n + 1 е.

f(n) = n³, g(n) = 6n + 1 е.

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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Can I get help on part e?

Part 3: Big-Oh? K. Suggested reading: Sections 2.1 and 2.2 of Algorithm Design. Below are four pairs of functions, labeled f and g. For each, determine constants a and no such that for all n > no, a· f(n) > g(n). Give a clear argument as to why your choice of no and a satisfy the conditions. а. f(n) — 2n + 3, g(n) = 5n b. f(n) = 2n + 3, g(n) = 5n + log(n) с. f(n) %3D п1/4, g(n) %3 1og(n) = d. f(n) %3D п, д(n) %3 (log2 n)4 е. f(n) — п3, g(n) — 6п + 1 = n Hint: you may assume that for all x > 0, log(x) < x.
Transcribed Image Text:Part 3: Big-Oh? K. Suggested reading: Sections 2.1 and 2.2 of Algorithm Design. Below are four pairs of functions, labeled f and g. For each, determine constants a and no such that for all n > no, a· f(n) > g(n). Give a clear argument as to why your choice of no and a satisfy the conditions. а. f(n) — 2n + 3, g(n) = 5n b. f(n) = 2n + 3, g(n) = 5n + log(n) с. f(n) %3D п1/4, g(n) %3 1og(n) = d. f(n) %3D п, д(n) %3 (log2 n)4 е. f(n) — п3, g(n) — 6п + 1 = n Hint: you may assume that for all x > 0, log(x) < x.
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Step 1: Given.

Given: e) f(n)=n3 and g(n)=6n+1

To find: a and n0 such that a·f(n)≥g(n)

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