Place these functions in order from slowest asymptotic growth to fastest asymptoticgrowth. Justify the claimed order for each pair of consecutive functions that appear in your orderedlist. For instance, if you claim that 𝑓𝑖(𝑛)

Question

Place these functions in order from slowest asymptotic growth to fastest asymptoticgrowth. Justify the claimed order for each pair of consecutive functions that appear in your orderedlist. For instance, if you claim that 𝑓𝑖(𝑛) < 𝑓𝑗(𝑛) ﻿in growth rate for some choice of the functions 𝑓𝑖(𝑛)and 𝑓𝑗(𝑛), ﻿show that the limit test yields lim𝑛→∞ 𝑓𝑖(𝑛)/𝑓𝑗(𝑛) = 0.Hint: Try and simplify the functions algebraically before comparing them.NB: The notation lg 𝑛 ﻿stands for log2 𝑛.Grading: This question will be graded according to the work you show. If you simply guess that 𝑓𝑖(𝑛) <𝑓𝑗(𝑛) ﻿without justification, or if the functions appear in the proper order by chance (for instance, ifyou claim that 𝑓𝑖(𝑛) < 𝑓𝑗(𝑛) < 𝑓𝑘(𝑛) ﻿and the justifications for 𝑓𝑖(𝑛) < 𝑓𝑗(𝑛) ﻿and/or 𝑓𝑗(𝑛) < 𝑓𝑘(𝑛)are missing or wrong (or if these orderings are themselves wrong), ﻿you will be docked points even ifit turns out that 𝑓𝑖(𝑛) < 𝑓𝑘(𝑛) ﻿by chance and/or without a proper justification). ﻿If all justifications arecorrect and correspond to consecutive functions on your ordered list, the grade will be the length ofthe longest common subsequence of functions between your solution and the expected (i.e. ﻿correct)solution.

Accepted Answer

To order the functions by their asymptotic growth ...

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