There's no limit to it

Calculus Level 4

\[\large \lim_{x\to0} \frac{ \cos^2 (x) - \cos (x) - e^x \cos(x) + e^x - \frac{x^3}2 }{x^n} \]

If the limit above is a finite non-zero number, find the minimum integer value of \(n\).

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