Problem

Evaluate.

(1) $\displaystyle \lim_{x \to 1} \frac{\sqrt[3]{x+7}-2}{1-\sqrt{x}} = \underline{\quad(1)\quad}$.

(2) $\displaystyle \lim_{x \to \infty} x \tan \frac{\pi}{x} \tan^{-1} \frac{x}{\pi} = \underline{\quad(2)\quad}$.