Question

PART 2 - Comparing the orders of growth between two algorithms (4pts) Say we have two different algorithms with respective runtimes of f(n) and g(n). Given the following cases, prove whether or not f(n) is O(g(n)) in each case. You need to show your work with the crucial steps, e.g. finding the necessary constant c in the definition of Big-O. You may utilize the pull-up/pull-down or the l'Hopital's trick discussed in class whenever needed. You will be penalized for up to 1 pt in total if all your work for this entire PART exceeds a whole A4/US letter page in 12px font size (assuming you start from the top of the page). P.S. sqrt(n) means the square root of n, aka n^(1/2). Case f(n) g(n) cos(n)+1 sin(n)+10

          PART 2 - Comparing the orders of growth between two algorithms (4pts)
Say we have two different algorithms with respective runtimes of f(n) and g(n). Given the following cases, prove whether or not f(n) is O(g(n)) in each case. 
You need to show your work with the crucial steps, e.g. finding the necessary constant c in the definition of Big-O. You may utilize the pull-up/pull-down or the l'Hopital's trick discussed in class whenever needed.
You will be penalized for up to 1 pt in total if all your work for this entire PART exceeds a whole A4/US letter page in 12px font size (assuming you start from the top of the page).
P.S. sqrt(n) means the square root of n, aka n^(1/2).
Case
f(n)
g(n)
cos(n)+1
sin(n)+10

Added by Kelsey S.

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