Nilai \( \displaystyle \lim_{x \to 0} \ \frac{x^2}{1-\sqrt{1+x^2}} = \cdots \)
- 2
- 0
- -1
- -2
- -3
(EBTANAS SMA IPA 2000)
Pembahasan:
\begin{aligned} \lim_{x \to 0} \ \frac{x^2}{1-\sqrt{1+x^2}} &= \lim_{x \to 0} \ \frac{x^2}{1-\sqrt{1+x^2}} \times \frac{1+\sqrt{1+x^2}}{1+\sqrt{1+x^2}} \\[8pt] &= \lim_{x \to 0} \ \frac{x^2(1+\sqrt{1+x^2})}{1-(1+x^2)} \\[8pt] &= \lim_{x \to 0} \ \frac{x^2(1+\sqrt{1+x^2})}{-x^2} \\[8pt] &= \lim_{x \to 0} \ -(1+\sqrt{1+x^2}) \\[8pt] &= -(1+\sqrt{1+0^2}) = -2 \end{aligned}
Jawaban D.