Nilai \( \displaystyle \lim_{x \to 2} \ \frac{\sqrt{3x-2}-2}{2x-4} = \cdots \)
- 0
- 3/8
- 3/4
- 1
- \( 1 \frac{1}{2} \)
(SNMPTN 2008)
Pembahasan:
\begin{aligned} \lim_{x \to 2} \ \frac{\sqrt{3x-2}-2}{2x-4} &= \lim_{x \to 2} \ \frac{\sqrt{3x-2}-2}{2x-4} \times \frac{\sqrt{3x-2}+2}{\sqrt{3x-2}+2} \\[8pt] &= \lim_{x \to 2} \ \frac{(3x-2)-4}{(2x-4)(\sqrt{3x-2}+2)} \\[8pt] &= \lim_{x \to 2} \ \frac{3(x-2)}{2(x-2)(\sqrt{3x-2}+2)} \\[8pt] &= \lim_{x \to 2} \ \frac{3}{2(\sqrt{3x-2}+2)} \\[8pt] &= \frac{3}{2(\sqrt{3(2)-2}+2)} \\[8pt] &= \frac{3}{8} \end{aligned}
Jawaban B.