Evaluate (lim limits_{x to 3} frac{x^{2} – 2x – 3}{x – 3})
-
A.
4 -
B.
3 -
C.
2 -
D.
0
Correct Answer: Option A
Explanation
(lim limits_{x to 3} frac{x^{2} – 2x – 3}{x – 3})
(frac{x^{2} – 2x – 3}{x – 3} = frac{x^{2} – 3x + x – 3}{x – 3})
(frac{(x – 3)(x + 1)}{x – 3} = x + 1)
(lim limits_{x to 3} frac{x^{2} – 2x – 3}{x – 3} equiv lim limits_{x to 3} (x + 1)) (L’Hopital rule)
(lim limits_{x to 3} (x + 1) = 3 + 1 = 4)