Q2. Assume the following function definitions: f.(n) = n log(nº0º) f.(n) = 2logn f:(n) = n\n fs(n) = (log log n) 100 fa(n) = log (n!) f.(n) = n/(log n)100 For each of the asymptotic relationships shown in the table below indicate whether it is TRUE or FALSE and state why. True/False Why? filn) is Qf£(n)) fa(n) is O(f:(1)) f:(n) is O(f6(n)) fa(n) is N(fi(n)) fi(n) is O(fi(n))

Q2. Assume the following function definitions: f.(n) = n log(nº0º) f.(n) = 2logn f:(n) = n\n fs(n) = (log log n) 100 fa(n) = log (n!) f.(n) = n/(log n)100 For each of the asymptotic relationships shown in the table below indicate whether it is TRUE or FALSE and state why. True/False Why? filn) is Qf£(n)) fa(n) is O(f:(1)) f:(n) is O(f6(n)) fa(n) is N(fi(n)) fi(n) is O(fi(n))

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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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

Q2. Assume the following function definitions:
f. (n)
f.(n) = 2logn
= n log(n100)
f-(n) = nyn
fa(n) = log (n!)
fs (n) = (log log n)10
100
f.(n) = n/(log n)100
For each of the asymptotic relationships shown in the table below indicate whether it is TRUE or
FALSE and state why.
True/False
Why?
fi(n) is Qfi(n))
fa(n) is O(fs(n))
fs(n) is O(fo(n))
fa(n) is fi(n))
fi(n) is O(f(n))

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