Nilai \( \displaystyle \lim_{x \to 2} \ \frac{x^2-5x+6}{x^2-4} = \cdots \)
- \( -\frac{1}{4} \)
- \( -\frac{1}{8} \)
- \( -\frac{1}{8} \)
- \( 1 \)
- \( \frac{5}{4} \)
(EBTANAS SMA IPA 2002)
Pembahasan:
\begin{aligned} \lim_{x \to 2} \ \frac{x^2-5x+6}{x^2-4} &= \lim_{x \to 2} \ \frac{(x-2)(x-3)}{(x-2)(x+2)} \\[8pt] &= \lim_{x \to 2} \ \frac{(x-3)}{(x+2)} \\[8pt] &= \frac{2-3}{2+2} = -\frac{1}{4} \end{aligned}
Jawaban A.