CSE250 HW3 Solution

# CSE250 HW3 Solution - CSE 250 Spring 2011 Homework 3 Due...

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CSE 250 Spring 2011 Homework 3 Due Date: March 21, Monday, by 2:05pm Total Points: 30 Due Time: 2:05’00” pm. Print your Name, UB #, and Recitation section on the frst page. IF these guidelines are not Followed, TA may deduct 10% oF points. 1. (10 pts) Order the following functions by growth rate. Indicate which functions grow at the same rate. Use limit test to justify your answer. N, N, N log N, N 2 / log N, N log( N 3 ) , 2 N , 2 N/ 3 Note: The easiest way to solve this problem is: First, arrange the functions in the order of increasing growth rate. Then, compare each pair of consecutive functions in the list. Solution : (1) N, N, N log N, N log( N 3 ) , N 2 / log N, 2 N/ 3 , 2 N where N log N and N log( N 3 ) grow at the same rate. (2) lim N →∞ N N = lim N →∞ 1 N = 0 lim N →∞ N N log N = lim N →∞ 1 log N = 0 lim N →∞ N log N N log( N 3 ) = lim N →∞ log N 3 log N = 1 3 lim N →∞ N log( N 3 ) N 2 / log N = lim N →∞ 3 log N log N N = lim N →∞ 3(log N ) 2 N = lim N →∞ 6 log N 1 N 1 = lim N →∞ 6 log N N = lim N →∞ 6 N = 0 Because N 2 / log N = o ( N 3 ), and lim N →∞ N 3 2 N/ 3 = lim N →∞ 3 N 2 2 N/ 3 ln 2 / 3 = lim N →∞ 6 N 2 N/ 3 ln 2 ln 2 / 9 = lim N →∞ 6 2 N/ 3 ln 2 ln 2 ln 2

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CSE250 HW3 Solution - CSE 250 Spring 2011 Homework 3 Due...

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