# A bit of everything

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.

×