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Solve the following problems- Problems 1 through 3 are about growth ra.docx

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Solve the following problems. Problems 1 through 3 are about growth rate of functions. Problem 4 is on analysis. Problems 5 through 7 are on design. 1. Prove that lo g ( n !) = ( n lo g n ) . 2. Let f ( n ) , g ( n ) be two asymptotically positive functions. Let h ( n ) (the maximum of the two functions at any point) be defined as given below. .

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Solve the following problems. Problems 1 through 3 are about growth rate of functions. Problem 4 is on analysis. Problems 5 through 7 are on design. 1. Prove that lo g ( n !) = ( n lo g n ) . 2. Let f ( n ) , g ( n ) be two asymptotically positive functions. Let h ( n ) (the maximum of the two functions at any point) be defined as given below.

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