Nilai \( \displaystyle \lim_{x \to 7} \ \frac{\sqrt{x}(x-7)}{\sqrt{x}-\sqrt{7}} = \cdots \)
- 14
- 7
- \( 2 \sqrt{7} \)
- \( \sqrt{7} \)
- \( \frac{1}{2} \sqrt{7} \)
(SPMB 2006)
Pembahasan:
\begin{aligned} \lim_{x \to 7} \ \frac{\sqrt{x}(x-7)}{\sqrt{x}-\sqrt{7}} &= \lim_{x \to 7} \ \frac{\sqrt{x}(x-7)}{\sqrt{x}-\sqrt{7}} \times \frac{\sqrt{x}+\sqrt{7}}{\sqrt{x}+\sqrt{7}} \\[8pt] &= \lim_{x \to 7} \ \frac{\sqrt{x}(x-7)(\sqrt{x}+\sqrt{7})}{x-7} \\[8pt] &= \lim_{x \to 7} \ \sqrt{x} \ (\sqrt{x}+\sqrt{7}) \\[8pt] &= \sqrt{7} \ (\sqrt{7}+\sqrt{7}) \\[8pt] &= \sqrt{7} \ (2\sqrt{7}) = 14 \end{aligned}
Jawaban A.