What is the value of [math] \displaystyle \lim_{x \to \tfrac{\pi}{3}} \frac{\sin\left(x-\tfrac{\pi}{3}\right)}{1 - 2 \cos x} [/math]?
What is the value of [math]\lim_{x\to\infty} x \cdot \{ \arctan \left(\frac{x+1}{x+4}\right) - \frac{\pi}{4} \} [/math]?