1. Give an example of function f(n) for which f(n+1)-f(n)-(2n 2. Insert the numbers 4, 5,8, 2,7,6,3, 1 in that sequence in an initially empty array-based heap, then do one deletemin, and draw the resulting tree. 3. Show that f(n) @n(f(n-1) + f(n-2), implies f(n) = 0((n + 1)!). 4. Show that f(n) Sn/(Vf) implies f(n) = 0( ). 5. List the comparisons that are made when executing mergesort on the unsorted array [6, 8,7, 2, 1,4,3, 5]