# Determine continuity

Calculus Level 3

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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