Nilai \( \displaystyle \lim_{x \to 2} \ \frac{2x^2-x-6}{3x^2-5x-2} = \cdots \)
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(UN SMA IPS 2018)
Pembahasan:
\begin{aligned} \lim_{x \to 2} \ \frac{2x^2-x-6}{3x^2-5x-2} &= \lim_{x \to 2} \ \frac{(2x+3)(x-2)}{(3x+1)(x-2)} \\[8pt] &= \lim_{x \to 2} \ \frac{(2x+3)}{(3x+1)} \\[8pt] &= \frac{2(2)+3}{3(2)+1} \\[8pt] &= 1 \end{aligned}
Jawaban D.