Solve 5 of 6 among the following problems P1 to P6 on asymptotic growth of functions. Solve problem P7. You may submit your solutions typed or neatly written by hand. P1. - P6.: For five selected problems: (a) Start with the definition you were given for O(_),(_), and (_)as needed form the problem at hand. For each problem determine the values of the constants in the formal definitions. (b) For your solved problems: for problems of O(_), determine whether o(_) also holds; for problems of (_), determine whether (_)also holds; for cases of (_), check for both o(_)and (_). P1.: Show formally that lgn2=(lgn+5) do (a) and (b) P2: Show formally that nlogn+5=(lgn) do (a) and (b) P3: Show formally that 2n=(10n2) do (a) and (b) P4: Show formally that 2n=O(3n) do (a) and (b) P5: Show formally that n33n2n+1=(n3) do (a) and (b) P6: Show formally that n2n+1=(n2/2) do (a) and (b)