Chapter 3.2, Problem 13E

Exercises 1—14, to establish a big-Orelationship, find witnessesCandksuch that $\left|f\left(x\right)\right|\le C\left|g\left(x\right)\right|$whenever $x>k$.

Show that $2^n$is $O\left(3^n\right)$but that $3^n$is not $O\left(2^n\right)$. (Note that this is a special case of Exercise 60.)(Requires calculus) Show that if $c>b>1$, then $b^n$is $O\left(c^n\right)$, but $c^n$is not $O\left(b^n\right)$