Nilai \( \displaystyle \lim_{x \to 4} \ \frac{x^2-16}{5-\sqrt{x^2+9}} = \cdots \)
- -20
- -10
- 0
- 8
- 20
(SPMB 2007)
Pembahasan:
\begin{aligned} \lim_{x \to 4} \ \frac{x^2-16}{5-\sqrt{x^2+9}} &= \lim_{x \to 4} \ \frac{x^2-16}{5-\sqrt{x^2+9}} \times \frac{5+\sqrt{x^2+9}}{5+\sqrt{x^2+9}} \\[8pt] &= \lim_{x \to 4} \ \frac{(x^2-16)(5+\sqrt{x^2+9})}{25-(x^2+9)} \\[8pt] &= \lim_{x \to 4} \ \frac{(x^2-16)(5+\sqrt{x^2+9})}{-(x^2-16)} \\[8pt] &= \lim_{x \to 4} \ -(5+\sqrt{x^2+9}) \\[8pt] &= -(5+\sqrt{4^2+9}) \\[8pt] &= -10 \end{aligned}
Jawaban B.