# 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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