Please complete the following parts

P1. Order the following functions by asymptotic growth rate. 4nlogn+2n3n+100lognn2+10n2104nn32logn2nnlogn Hint: Simplify the expressions, and then use the ordering of the seven important algorithmanalysis functions to order this set. P2. Show that (n+1)5 is O(n5). Hint: Notice that (n+1)2n for n1. P3. Show that 2n+1 is 0(2n). Hint: 2n+1=22a P4. An evil king has n bottles of wine, and a spy has just poisoned one of them. Unfortunately, they do not know which one it is. The poison is very deadly; just one drop diluted even a billion to one will still kill. Even so, it takes a full month for the poison to take effect. Design a scheme for determining exactly which one of the wine bottles was poisoned in just one month's time while expending O (logn) taste testers. Hint: Number each bottle and think about the binary expansion of each bottle's number. P5. Give a big-Oh characterization, in terms of n, of the running time of the example5 method shown in Code Fragment below: Hint: Consider the number of times the inner loop is executed and how many primitive operations occur in each iteration, and then do the same for the two outer loops