Chapter 3.2, Problem 62E

1. (Requires calculus) Prove or disprove that (2n)! isO(n!).

The following problems deal with another type of asymptotic notation, calledlittle-onotation. Because little-onotation is based on the concept of limits, a knowledge of calculus is needed for these problems. We say that $f\left(x\right)$is $o\left(g\left(x\right)\right)$[read $f\left(x\right)$is “little-oh” of $g\left(x\right)$],

when

$\underset{x\to \infty }{\lim }\frac{f\left(x\right)}{g\left(x\right)}=0$