Find the integral value of n for which x→0limxncos2x−cosx−excosx+ex−2x3 is a finite nonzero number

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Question

Find the integral value of $n$ for which $x \to 0 lim \frac{cos ^{2} x - cos x - e ^{x} cos x + e ^{x} - \frac{x ^{3}}{2}}{x ^{n}}$ is a finite nonzero number

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Daniel Discussed

Find the integral value of

n

for which

x \to 0 lim \frac{cos ^{2} x - cos x - e ^{x} cos x + e ^{x} - \frac{x ^{3}}{2}}{x ^{n}}

is a finite nonzero number

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Question Text

Find the integral value of

n

for which

x \to 0 lim \frac{cos ^{2} x - cos x - e ^{x} cos x + e ^{x} - \frac{x ^{3}}{2}}{x ^{n}}

is a finite nonzero number