Nilai \( \displaystyle \lim_{x \to 3} \ \frac{(x-3)(\sqrt{x}+\sqrt{3})}{\sqrt{x}-\sqrt{3}} = \cdots \)
- 0
- 3
- 6
- 12
- 15
(SPMB 2004)
Pembahasan:
\begin{aligned} \lim_{x \to 3} \ \frac{(x-3)(\sqrt{x}+\sqrt{3})}{\sqrt{x}-\sqrt{3}} &= \lim_{x \to 3} \ \frac{(\sqrt{x}-\sqrt{3})(\sqrt{x}+\sqrt{3})(\sqrt{x}+\sqrt{3})}{\sqrt{x}-\sqrt{3}} \\[8pt] &= \lim_{x \to 3} \ (\sqrt{x}+\sqrt{3})(\sqrt{x}+\sqrt{3}) \\[8pt] &= (\sqrt{3}+\sqrt{3})(\sqrt{3}+\sqrt{3}) \\[8pt] &= (2\sqrt{3}) (2\sqrt{3}) = 4 \cdot 3 \\[8pt] &= 12 \end{aligned}
Jawaban D.