Nilai \( \displaystyle \lim_{x \to 0} \ \frac{\sqrt{4x}}{\sqrt{\sin 2x}} = \cdots \)
- \( \sqrt{2} \)
- 1
- 1/2
- 1/4
- 0
(SNMPTN 2010)
Pembahasan:
\begin{aligned} \lim_{x \to 0} \ \frac{\sqrt{4x}}{\sqrt{\sin 2x}} &= \lim_{x \to 0} \ \sqrt{\frac{4x}{\sin 2x}} \\[8pt] &= \sqrt{ \lim_{x \to 0} \ \frac{4x}{\sin 2x} } \\[8pt] &= \sqrt{\frac{4}{2}} = \sqrt{2} \end{aligned}
Jawaban A.