Evaluate \(\lim \limits_{x \to 2} \frac{(x - 2)(x^2 + 3x - 2)}{x^2 - 4}\)
A
7
B
2
C
3
D
4
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\lim \limits_{x \to 2} \frac{(x - 2)(x^2 + 3x - 2)}{x^2 - 4}\)
\(\frac{(x - 2)(x^{2} + 3x - 2)}{x^{2} - 4} = \frac{(x - 2)(x^{2} + 3x - 2)}{(x - 2)(x + 2)}\)
= \(\frac{(x^{2} + 3x - 2)}{x + 2}\)
\(\therefore \lim \limits_{x \to 2} \frac{(x - 2)(x^2 + 3x - 2)}{x^2 - 4} = \lim \limits_{x \to 2} \frac{x^{2} + 3x - 2}{x + 2}\)
= \(\frac{2^{2} + 3(2) - 2}{2 + 2}\)
= \(\frac{4 + 6 - 2}{4}\) = 2
Source: Myschool Past Questions Archive (Record #31350)