Let's do some calculus! (28)

Calculus Level 5

$\large {\lim_{x \to 0}} \ \dfrac{\cos^2 x - \cos x - e^x \cos x + e^x - \dfrac{x^3}{2}}{x^n}$

Find the value of $n$ for which the above limit is finite and non-zero.

Notations: $e \approx 2.71828$ is the Euler's number.