a. Table 2.1 contains values of several functions that often arise in the analysis of algorithms....

a. Table 2.1 contains values of several functions that often arise in the analysis of algorithms. These values certainly suggest that the functions

log n, n, n log₂ n, n², n³, 2ⁿ, n!

are listed in increasing order of their order of growth. Do these values prove this fact with mathematical certainty?

b. Prove that the functions are indeed listed in increasing order of their order of growth.

TABLE 2.1 Values (some approximate) of several functions important for analysis of algorithms