# Integral limit

Calculus Level 3

$\large \displaystyle \lim_{x \rightarrow 0} \dfrac{ ( 1 - \cos x)(\cos x - e^x)}{x^{\color{#3D99F6}n}}$

Find the integer $\color{#3D99F6}n$ for which above limit is a finite non-zero number.

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