Let $F(t)=\frac{t^2-t-12}{t+3}i+\frac{t+4}{t-4}j+\frac{(t+3{)}^2}{sin(t+3)}k,$ find $\underset{t-3}{lim}F(t)$

A$.($:$-7,\frac{1}{-7},1$:$)$

B$.$ Does not exist

c$.($:$\frac{0}{0},\frac{1}{-7},\frac{0}{0}$:$)$

D$.($:$-7,\frac{1}{-7},0$:$)$

E$.($:$3,\frac{1}{-7},1$:$)$