Nilai \( \displaystyle \lim_{x \to 2} \ \frac{4-x^2}{3-\sqrt{x^2+5}} = \cdots \)
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(UN SMA IPA 2003)
Pembahasan:
\begin{aligned} \lim_{x \to 2} \ \frac{4-x^2}{3-\sqrt{x^2+5}} &= \lim_{x \to 2} \ \frac{4-x^2}{3-\sqrt{x^2+5}} \times \frac{3+\sqrt{x^2+5}}{3+\sqrt{x^2+5}} \\[8pt] &= \lim_{x \to 2} \ \frac{(4-x^2)(3+\sqrt{x^2+5})}{9-(x^2+5)} \\[8pt] &= \lim_{x \to 2} \ \frac{(4-x^2)(3+\sqrt{x^2+5})}{4-x^2} \\[8pt] &= \lim_{x \to 2} \ (3+\sqrt{x^2+5}) \\[8pt] &= 3+\sqrt{2^2+5} = 3 + \sqrt{9} \\[8pt] &= 6 \end{aligned}
Jawaban E.