$4.$ a$.$ Table $2\mathrm{.}1$ contains values of several functions that often arise in the analysisof algorithms. These values certainly suggest that the functionslog n$,$ n$,$ n log $2$ n$,$ n$2,$ n$3,2$n $,$ n$!$are listed in increasing order of their order of growth. Do these valuesprove this fact with mathematical certainty?b$.$ Prove that the functions are indeed listed in increasing order of their orderof growth