1. (25 points) Arrange the following list of functions in ascending order of growth rate. Note that two functions may have the same asymptotic growth rate! Prove the relationship of every pair of adjacent functions in your ordered list, including functions that have the same growth rate => 7 proofs for the following list. For example, with order fi(n)=n, f:(n) = n, f3(n)=n4, one must prove that nis O(n?) and n is O(n^) but after so doing there is no need (because of transitivity) to show that n is O(n^). fa(n) = n + 100000 fi(n) = 22 fe(n) = n2 (log n) fa(n) = 21 fe(n) =(4/(34) ff(n) = log in fe(n)=(n)52 fi(n) =n * 10 May use any of the following to support your ordering Definition of big Q => with definitive constants and sample progression of values I Limits L'Hopital's Rule alongside limits