# Integral limit

**Calculus**Level 3

\[ \large \displaystyle \lim_{x \rightarrow 0} \dfrac{ ( 1 - \cos x)(\cos x - e^x)}{x^{\color{blue}n}}\]

Find the integer \(\color{blue}n\) for which above limit is a finite non-zero number.

\[ \large \displaystyle \lim_{x \rightarrow 0} \dfrac{ ( 1 - \cos x)(\cos x - e^x)}{x^{\color{blue}n}}\]

Find the integer \(\color{blue}n\) for which above limit is a finite non-zero number.

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