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Unformatted text preview: f. (1 Point) ) ! lg( n ) lg( n n 2 5. (4 Points) p.58: 3-4cdeh Let ) ( n f and ) ( n g be asymptotically positive functions (i.e. ) ( > n f and ) ( > n g for sufficiently large n .) Prove or disprove the following statements. c. (1 Point) Assume 1 )) ( lg( ≥ n g and 1 ) ( ≥ n f for all sufficiently large n . Then )) ( ( ) ( n g O n f = implies ))) ( (lg( )) ( lg( n g O n f = . d. (1 Point) )) ( ( ) ( n g O n f = implies ) 2 ( 2 ) ( ) ( n g n f O = . e. (1 Point) ) )) ( (( ) ( 2 n f O n f = . h. (1 Point) )) ( ( )) ( ( ) ( n f n f o n f Θ = + . 6. (1 Point) Let ) ( ) ( n n f Θ = . Prove that ) ( ) ( 2 1 n i f n i Θ = ∑ = . (See the hint at bottom of p.4 of the handout on asymptotic growth rates.)...
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- Spring '09
- Following, Sufficiently large