A calculus problem by Ryan Broder

Calculus Level 5

f(x)=limn+ k=1ncosx2kf(x) = \lim_{n \to +\infty} \ \prod_{k=1}^{n} \cos{\frac{x}{2^k}} lima+x=aaf(x)=N\lim_{a \to +\infty} \sum_{x=-a}^{a} f(x)=N What is 100N\lfloor {100N} \rfloor?

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