# Find the limit of composition 1

Calculus Level 3

A function is defined as $$f(x)=\sin x$$ and $$f \circ f \circ f \circ \cdots \circ f(x)=f_n (x)$$, where $$n$$ is the number of compositions, for all real $$x$$.

Find $$\displaystyle \lim_{n \to \infty} f_n (x)$$.

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