Let $F(t)=\frac{t^3+1}{t+1}i+\frac{tan(t+1)}{t+1}j+(t^2-5)e^{t^2-1}k,$ find $\underset{t-1}{lim}F(t).$

$A.($:$\frac{0}{0},\frac{0}{0},0$:$)$

$B.($:$0,0,0$:$)$

$C.$ Does not exist

$D.($:$3,1,-4$:$)$

$E.($:$0,1,-4$:$)$