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For each positive integer nnn, let
fn(x)=sin(fn−1(x)), f^n (x) = \sin ( f^{n-1} (x) ), fn(x)=sin(fn−1(x)),
with f0(x)=x f^0 (x) = x f0(x)=x.
Let y(x)=limn→∞fn(x) y(x) = \lim_{n \rightarrow \infty } f^n(x) y(x)=limn→∞fn(x).
Determine y′(0) y'(0) y′(0).
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