JEE-Advanced 2015 (25/40)

Calculus Level 3

Let \(m\) and \(n\) be two positive integers greater than 1. Find the value of \(\frac{m}{n}\) if \[\displaystyle \lim_{\alpha \to 0} \left( \dfrac{e^{\cos(\alpha^n)}-e}{\alpha^m} \right)=-\frac{e}{2}\]

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