MIT6_042JS10_lec25_prob

# MIT6_042JS10_lec25_prob - Massachusetts Institute of...

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Unformatted text preview: Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science April 7 Prof. Albert R. Meyer revised March 31, 2010, 99 minutes In-Class Problems Week 9, Wed. Problem 1. Recall that for functions f,g on N , f = O ( g ) iff ∃ c ∈ N ∃ n ∈ N ∀ n ≥ n c · g ( n ) ≥ | f ( n ) | . (1) For each pair of functions below, determine whether f = O ( g ) and whether g = O ( f ) . In cases where one function is O() of the other, indicate the smallest nonegative integer , c , and for that small- est c , the smallest corresponding nonegative integer n ensuring that condition ( 1 ) applies. (a) f ( n ) = n 2 ,g ( n ) = 3 n . f = O ( g ) YES NO If YES, c = , n = g = O ( f ) YES NO If YES, c = , n = (b) f ( n ) = (3 n − 7) / ( n + 4) ,g ( n ) = 4 f = O ( g ) YES NO If YES, c = , n = g = O ( f ) YES NO If YES, c = , n = (c) f ( n ) = 1 + ( n sin( nπ/ 2)) 2 ,g ( n ) = 3 n f = O ( g ) YES NO If yes, c = n = g = O ( f ) YES NO If yes, c = n = Problem 2.2....
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MIT6_042JS10_lec25_prob - Massachusetts Institute of...

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