# What are sine and cosine doing here?

Calculus Level 5

$\large \lim_{x \to \infty} \dfrac{f^{-1}(1000x)-f^{-1}(x)}{\sqrt [3]{x}}$

Let $$f(x) = 27x^3 + (\cos13 + \sin13) x$$, and let $$f^{-1}(x)$$ denote the inverse function of $$f(x)$$.
Compute the limit above.

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