Evaluate a given limit Evaluate the following limit:
$$\lim_{x \rightarrow 4} \left( \frac{1}{13 - 3x} \right) ^ {\tan \frac{\pi x}{8}}$$
I haven't managed to get anything meaningful yet.
Thank you in advance!

see my nice answer:
assume $x=t+4$ $$\lim_{x \rightarrow 4} \left( \frac{1}{13 - 3x} \right) ^ {\tan \frac{\pi x}{8}}=\lim_{t \to 0} \left( \frac{1}{13 - 3(t+4)} \right) ^ {\tan \frac{\pi (t+4)}{8}}$$
$$=\lim_{t \to 0} \left( \frac{1}{1-3t} \right) ^ {-\cot \frac{\pi t}{8}}$$
$$=\lim_{t \to 0} \left(1-3t \right) ^ {\cot \frac{\pi t}{8}}$$
above limit has form $1^{\infty}$, so
$$=e^{\large \lim_{t \to 0} \left(1-3t-1 \right) \cdot {\cot \frac{\pi t}{8}}}$$
$$=e^{\large \lim_{t \to 0} \left(-3t\right) \cdot {\cot \frac{\pi t}{8}}}$$
$$=e^{\large-3\cdot \frac{8}{\pi}\lim_{t \to 0}  \frac{\frac{\pi t}{8}}{\tan\frac{\pi t}{8}}}=e^{-24/\pi}$$
