Evaluate (lim limits_{x to 2} frac{(x – 2)(x^2 + 3x – 2)}{x^2 – 4})
-
A.
7 -
B.
2 -
C.
3 -
D.
4
Correct Answer: Option B
Explanation
(lim limits_{x to 2} frac{(x – 2)(x^2 + 3x – 2)}{x^2 – 4})
(frac{(x – 2)(x^{2} + 3x – 2)}{x^{2} – 4} = frac{(x – 2)(x^{2} + 3x – 2)}{(x – 2)(x + 2)})
= (frac{(x^{2} + 3x – 2)}{x + 2})
(therefore lim limits_{x to 2} frac{(x – 2)(x^2 + 3x – 2)}{x^2 – 4} = lim limits_{x to 2} frac{x^{2} + 3x – 2}{x + 2})
= (frac{2^{2} + 3(2) – 2}{2 + 2})
= (frac{4 + 6 – 2}{4} = 2)