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The solutions and problems for a group exercise in cecs 228, due on december 7, 2004. The exercise includes finding the least integer n for the big o notation of given functions, showing that the sum of the product of a positive integer k and the first n natural numbers is o(nk+1), and describing an algorithm to find the longest word in an english sentence.
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Due 12/7/ Group members:____________________________________________________________________________
1. Problem 8 in Section 2. Find the least integer n such that f ( x ) is O( x n) for each of the following functions. Support your answer. a) f ( x ) = 2 x^2 + x^3 log x b) f ( x ) = 3 x^5 + (log x )^4 c) f ( x ) = ( x^4 + x^2 + 1) / (( x^4 + 1) d) f ( x ) = ( x^3 + 5 log x ) / ( x^4 + 1)
2. Problem 18 in Section 2. Let k be a positive integer. Show that 1k^ + 2k^ + … + nk^ **is O(nk+1).
