Determine continuity

Calculus Level pending

Is the following function \(f(x)\) continuous at \(x=0:\) (use \(\sin2x= 2 \sin x \cos x\))

\[ \mathit{f}(x) = \lim_{n \rightarrow \infty}\left(\cos x \cdot \cos \frac{x}{2} \cdot \cos \frac{x}{2^2} \cdot \cdot\cdot\cdot \cdot \cos \frac{x}{2^n} \right) ?\]

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