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Calculus Level 5

\[ \lim_{x\to\infty} \left [\dfrac{(( f(x) + 1) \left( 2f(x) + \dfrac32\right) (4f(x) + 1) )^{1/3} - f(x)}{f(x)} \right]^{x(x-2f(x))} \]

Let \(f: [0,\infty) \rightarrow [-4,\infty) \) be a function with an asymptote \(2y - x+3 = 0 \). Compute the limit above.

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