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Let f and g be functions such that: f(x) = 2r² log(r³), where : R→R • g(x) = 32³, where g: R → R (a) Determine whether f(x) is O(g(x)). Justify your answer using wit- nesses. If f(r) is not O(g(x)), then show an argument using a proof by contradiction using witnesses as to why f(x) is not O(g(x)). (b) Determine whether g(r) is O(f(x)). Justify your answer using wit- nesses.If g(r) is not O(f(z)), then show an argument using a proof by contradiction using witnesses as to why g(z) is not O(f(x)).

Let f and g be functions such that: f(x) = 2r² log(r³), where : R→R • g(x) = 32³, where g: R → R (a) Determine whether f(x) is O(g(x)). Justify your answer using wit- nesses. If f(r) is not O(g(x)), then show an argument using a proof by contradiction using witnesses as to why f(x) is not O(g(x)). (b) Determine whether g(r) is O(f(x)). Justify your answer using wit- nesses.If g(r) is not O(f(z)), then show an argument using a proof by contradiction using witnesses as to why g(z) is not O(f(x)).

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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This is Discreet math please answer questions with proper formatting for proofs
Let f and g be functions such that: • f(x) = 2x² log(x³), where f: R → R g(x) = 3r³, where g: R → R (a) Determine whether f(x) is O(g(x)). Justify your answer using wit- nesses. If f(r) is not O(g(x)), then show an argument using a proof by contradiction using witnesses as to why f(x) is not O(g(x)). (b) Determine whether g(r) is O(f(x)). Justify your answer using wit- nesses.If g(x) is not O(f(z)), then show an argument using a proof by contradiction using witnesses as to why g(r) is not O(f(x)).
Transcribed Image Text:Let f and g be functions such that: • f(x) = 2x² log(x³), where f: R → R g(x) = 3r³, where g: R → R (a) Determine whether f(x) is O(g(x)). Justify your answer using wit- nesses. If f(r) is not O(g(x)), then show an argument using a proof by contradiction using witnesses as to why f(x) is not O(g(x)). (b) Determine whether g(r) is O(f(x)). Justify your answer using wit- nesses.If g(x) is not O(f(z)), then show an argument using a proof by contradiction using witnesses as to why g(r) is not O(f(x)).
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