Determine whether the sequence converges or diverges. If the sequence converges, find its limit$.$

$($a$)\{\frac{n^3-2n+1}{5-6n^2+8n^3}{\}}_n=0^{}$

$($f$)\{\frac{n^2+(-1{)}^n}{3n-6n^2}{\}}_n=1^{}$

$($b$)\{nsin(\frac{}{n}){\}}_n=1^{}$

$($g$)\{\frac{n!}{n^n}{\}}_n=1^{}$

$($c$)\{\frac{e^n}{n!+1}{\}}_n=0^{}$

$($h$)\{\frac{cos(n)}{n}{\}}_n=1^{}$

$($d$)\{sin(\frac{n}{4}){\}}_n=0^{}$

$($i$)\{\frac{\sqrt[\phantom{2}]{n^4+n^2+1}}{n^2-2}{\}}_n=0^{}$

$($e$)\{{\displaystyle \underset{-n}{\overset{n}{}}}\frac{1}{1+t^2}(d)t{\}}_n=1^{}$

$($j$)\{(\frac{n+1}{n}{)}^n{\}}_n=1^{}$