Nilai \( \displaystyle \lim_{x \to 3} \ \frac{9-x^2}{4-\sqrt{x^2+7}} = \cdots \)
- 0
- 1
- 6
- 8
- ∞
(UM UGM 2004)
Pembahasan:
\begin{aligned} \lim_{x \to 3} \ \frac{9-x^2}{4-\sqrt{x^2+7}} &= \lim_{x \to 3} \ \frac{9-x^2}{4-\sqrt{x^2+7}} \times \frac{4+\sqrt{x^2+7}}{4+\sqrt{x^2+7}} \\[8pt] &= \lim_{x \to 3} \ \frac{(9-x^2)(4+\sqrt{x^2+7})}{16-(x^2+7)} \\[8pt] &= \lim_{x \to 3} \ \frac{(9-x^2)(4+\sqrt{x^2+7})}{9-x^2} \\[8pt] &= \lim_{x \to 3} \ (4+\sqrt{x^2+7}) \\[8pt] &= 4 + \sqrt{3^2+7} = 8 \end{aligned}
Jawaban D.