(a)  n   4n^2   f(n)=5n^2-3n+12   5n^2   upper holds?
    1      4                14      5   no
    2     16                26     20   no
    3     36                48     45   no
    4     64                80     80   yes
    5    100               122    125   yes
    6    144               174    180   yes
     violations for 4 <= n <= 10^6: 0
(c)  c          first n with 4^n > c*2^n
     10         4
     1000       10
     1000000    20
(d)  n        lg(n!)      (1/4)n lg n     n lg n
     4                4.58          2.00          8.00
     16              44.25         16.00         64.00
     1024          8769.01       2560.00      10240.00
     1048576   19458755.93    5242880.00   20971520.00
     violations for 4 <= n <= 10^6: 0
