Rodd and Todd

Calculus Level 4

\[ \lim_{x\to0} \dfrac{x - f_{2016}(x)}{x^3} \]

We define a recurrence relation, \(f_n(x) = \sin(f_{n-1}(x)) \) for \(n=2,3,4,\ldots\), with \(f_1(x) = \sin(x) \). Evaluate the limit above.

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