Answer the following questions\\
(a) Evaluate
$$\lim_{x \rightarrow 0^{+}} \left( x^{x^{x}} - x^{x} \right)$$
(b) Let $A = \frac{2\pi}{9}$, i.e., $A = 40$ degrees. Calculate the following
$$1 + \cos A + \cos 2A + \cos 4A + \cos 5A + \cos 7A + \cos 8A$$
(c) Find the number of solutions to $e^{x} = \frac{x}{2017} + 1$.