R-4.13 Order the following functions by asymptotic growth rate. 4nlogn+2n 210 2logn 3n+100logn 4n 2n n + 10n n nlogn R-4.14 Show that if d(n) is O(f(n)), then ad(n) is O(f(n)), for any constant a > 0. R-4.15 Show that if d(n) is O(f(n)) and e(n) is O(g(n)), then the product d(n)e(n) is O(f(n)g(n)). R-4.16 Give a big-Oh characterization, in terms of n, of the running time of the Ex1 function shown in Code Fragment 4.6. R-4.17 Give a big-Oh characterization, in terms of n, of the running time of the Ex2 function shown in Code Fragment 4.6. R-4.18 Give a big-Oh characterization, in terms of n, of the running time of the Ex3 function shown in Code Fragment 4.6. R-4.19 Give a big-Oh characterization, in terms of n, of the running time of the Ex4 function shown in Code Fragment 4.6. R-4.20 Give a big-Oh characterization, in terms of n, of the running time of the Ex5 function shown in Code Fragment 4.6.