The integer n for which x→0limxn(cosx−1)(cosx−ex) is finite nonzero number is ________

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The integer $n$ for which $x \to 0 lim \frac{( cos x - 1 ) ( cos x - e ^{x} )}{x ^{n}}$ is finite nonzero number is ________

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The integer

n

for which

x \to 0 lim \frac{( cos x - 1 ) ( cos x - e ^{x} )}{x ^{n}}

is finite nonzero number is ________

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Question Text

The integer

n

for which

x \to 0 lim \frac{( cos x - 1 ) ( cos x - e ^{x} )}{x ^{n}}

is finite nonzero number is ________