Let $f : (0, \infty) \rightarrow \mathbb{R}$ be defined by $$f(x) = \lim_{n \rightarrow \infty} \cos^{n}\left(\frac{1}{n^{x}}\right)$$ (a) Show that $f$ has exactly one point of discontinuity. (b) Evaluate $f$ at its point of discontinuity.
Let $f : (0, \infty) \rightarrow \mathbb{R}$ be defined by
$$f(x) = \lim_{n \rightarrow \infty} \cos^{n}\left(\frac{1}{n^{x}}\right)$$
(a) Show that $f$ has exactly one point of discontinuity.\\
(b) Evaluate $f$ at its point of discontinuity.