Let's do some calculus! (28)

Calculus Level 5

lim⁡x→0 cos⁡2x−cos⁡x−excos⁡x+ex−x32xn \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 nn for which the above limit is finite and non-zero.

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

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Tapas Mazumdar by Tapas Mazumdar
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