(a) Order the following functions by growth rates: N,N,N1.5,N2,NlogN,NloglogN,Nlog2N,Nlog(N2),2/N,2N,2N/2,37,N3,N2logN. Indicate which functions grow at the same rate. (b) Rank the following three functions: logN,log(N2),log2N. Explain. You should find all the mathematics you need in the class notes and in Kleinberg and Tardos, chapter 2. You may find it useful to remember that one way to compare the relative growth rates of f(n) and g(n) is to look at the ratio f(n)/g(n) as n. If that ratio approaches 0 , then g grows faster than f : f(n)=O(g(n)). If it approaches infinity then f grows faster than g. If the ratio approaches a constant different from both 0 and then f and g grow at the same rate