This is on a review for a calc 3 midterm. Could you please explain both questions? Thank you

2. Which of the following is the domain of the vector function r(t) = t In (t - 1) , V9 - 12, et ) ? (a) (1, 2) U (2, 3] (b) (1, 2) U (2, 3) (c) (1, 3] (d) [-3, 3] (e) (-3, 3) t 3. Find lim sin (it) 1 t -+ 0 t 2 + 3t' In(t + 1)' 2t (a) (0, -1, 1) (b )