Let $\{ f_{n}\}$ be a sequence of functions defined as follows:
$$f_{n}(x) = x^{n} \cos (2 \pi nx), \; x \in [ – 1, 1].$$
Then $\lim_{x \rightarrow 0} f_{n} (x)$ exists if and only if $x$ belongs to the interval
- $( – 1, 1)$
- $[ – 1, 1)$
- $[0, 1]$
- $( – 1, 1]$
