Which of the following continuous functions $f:\left ( 0,\infty \right ) \rightarrow \mathbb{R}$ can be extended to a continuous function on $\left [ 0,\infty \right )$ ?
- $f\left ( x \right )=sin\frac{1}{x}$
- $f\left ( x \right )=\frac{1-cos\:x}{x^{2}}$
- $f\left ( x \right )=cos\frac{1}{x}$
- $f\left ( x \right )=\frac{1}{x}$
