# Squeeze it repeatedly

Calculus Level 5

$\large \lim_{x\to 0} \frac{ f^{10000} (x)}{x^m}$

Define $$f(x) = 1 -\cos(x)$$ and the composite function $$f^n(x) = \underbrace{f \circ f \circ \ldots \circ f}_{n \text{ times}}$$.

If the limit above equals to non-zero finite number $$\frac1{L}$$ for a certain constant $$m$$. Evaluate $$\log_{32} \log_2 (2L)$$.

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