Nilai \( \displaystyle \lim_{x\to 2} \ \frac{(x-2) \cos (\pi x- 2 \pi)}{\tan (2\pi x - 4 \pi)} = \cdots \)
- \( -\frac{1}{2\pi} \)
- \( -\frac{1}{\pi} \)
- \( 0 \)
- \( \frac{1}{\pi} \)
- \( \frac{1}{2\pi} \)
Pembahasan:
\begin{aligned} \lim_{x\to 2} \ \frac{(x-2) \cos (\pi x- 2 \pi)}{\tan (2\pi x - 4 \pi)} &= \lim_{x\to 2} \ \frac{(x-2) \ \cos \pi (x- 2)}{\tan 2\pi (x - 2)} \\[8pt] &= \lim_{x\to 2} \ \cos \pi (x- 2) \cdot \lim_{x\to 2} \ \frac{(x-2)}{\tan 2\pi (x - 2)} \\[8pt] &= \cos \pi(0) \cdot \frac{1}{2\pi} = \cos 0 \cdot \frac{1}{2\pi} \\[8pt] &= 1 \cdot \frac{1}{2\pi} = \frac{1}{2\pi} \end{aligned}
Jawaban E.