Nilai \( \displaystyle \lim_{x\to 0} \ \frac{\tan 2x \cdot \tan 3x}{3x^2} = \cdots \)
- 0
- 2/3
- 3/2
- 2
- 6
Pembahasan:
\begin{aligned} \lim_{x\to 0} \ \frac{\tan 2x \cdot \tan 3x}{3x^2} &= \frac{1}{3} \cdot \lim_{x\to 0} \ \frac{\tan 2x}{x} \cdot \lim_{x\to 0} \ \frac{\tan 3x}{x} \\[8pt] &= \frac{1}{3} \cdot \frac{2}{1} \cdot \frac{3}{1} \\[8pt] &= 2 \end{aligned}
Jawaban D.