Let $a_n=\frac{3n-cos(n)}{n^3}$ and $b_n=\frac{1}{n^2}.$ Calculate the following limit$.$

$($Express numbers in exact form. Use symbolic notation and fractions where needed. Eater DNE if the limit does not exist

$L=\underset{x}{lim}{?}^e$

Determine the convergence of ${\displaystyle \underset{==1}{\overset{}{}}}{a}_{}.$

${\displaystyle \underset{?}{\overset{?}{}}}=-1a_0$ diverges by the Limit Comparison Teat since ${\displaystyle \underset{=1}{\overset{=}{}}}{b}_n$ converges and $\underset{s,-}{lim}\frac{a_s}{b_s}$ does not crist.

${\displaystyle \underset{?}{\overset{?}{}}}-a_n$ comorges by the Limit Comparison Test since ${\displaystyle \underset{?}{\overset{?}{}}}-{}^{-},{\displaystyle \underset{n}{\overset{?}{}}}$ comerges.

${\displaystyle \underset{-1}{\overset{}{}}}{a}_s$ diverges by the Limit Comparison Test since ${\displaystyle \underset{-}{\overset{}{}}}{b}_s$ diverges and $\underset{-}{lim}=\frac{a_s}{b_s}$ exists and is finite.

${\displaystyle \underset{-1}{\overset{}{}}}{}_4$ diverges by the Limit Comparison Test since ${\displaystyle \underset{-1}{\overset{}{}}}{b}_4$ diverges and $\underset{20}{lim}=\frac{{}_2}{h_8}$ is infinite.