$2.(6$ marks$)$ Find the limit: $($a$)$ limt$1$ t $2$t t$1,$ t $+8,$ sin t ln t $($b$)$ limt$$ te$$t $,$ t $3+$t $2$t $31,$ tsin $1$ t $($c$)$ limt$$e $2($tln t$,$ ln t t $2,$ p ln$($t $2))$