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) c. f(n) = n'/4, g(n) = log(n) %3D d. f(n) = n, g(n) = (log2 n)ª

Linear Algebra: A Modern Introduction
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Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
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Can someone help me with part d?

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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