The following questions are on the asymptotic growth of functions. Let n P. wher

Question

The following questions are on the asymptotic growth of functions. Let n P. where P is the set of positive integers {1,2,3,...} In each of the following situations, indicate whether f = O ( g ) . or f = o ( g ) . or f = Ohm ( g ) . or f = theta ( g ) . f ( n ) g ( n ) ( n - 100 ) ( n - 200 ) n log n 10nlog ( 10n ) 1og2n log 3n 10 log n log ( n2 ) n1.01 n log2 n n2 / log n n ( log n ) 2 ( log n ) log n n / log n n ( log n ) 3 n1 / 2 5logn n2n 3n 2n 2n + 1 ( log n ) log n2log n ) 2 n i = 1 ik nk + 1

Explanation / Answer

a) O,?,O b) same as a c) same as a d) same as a e) o,O
f) o,O g) o,O h)O i)o,O j)o,O k)o,O l)O,O,? m)o,O n)o,O Basically u need to find limit of g/f for n tending to 8. If the limit is a finite number then f = O(g),O(g),?(g) If the limit is 8 then f = O(g),o(g) if the limit is 0 then f = O(g)

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