Chapter 8.2, Problem 28E

(a)

To determine

To prove: If $\underset{n\to \infty }{lim}\frac{f\left(n\right)}{g\left(n\right)}=0$, then $f\prec g$.

(b)

To determine

To prove: If $\underset{n\to \infty }{lim}\frac{f\left(n\right)}{g\left(n\right)}=\infty$, then $g\prec f$.

(c)

To determine

To prove: If $\underset{n\to \infty }{lim}\frac{f\left(n\right)}{g\left(n\right)}=L$, for some $L\ne 0$, the $f\asymp g$.