Evaluate the limit for r$($t$)=($:t$^(-4),$sin$($t$),-6$:$).$

$\backslash$lim$\_($h$->0)($r$($t$+$h$)-$r$($t$))/($h$)=($:f$($t$),$g$($t$),$h$($t$)$:$)$

$($Use symbolic notation and fractions where needed.$)$

f$($t$)=$

g$($t$)=$

h$($t$)=$