JEE-Advanced 2015 (25/40)

Calculus Level 2

Let mm and nn be two positive integers greater than 1. Find the value of mn\frac{m}{n} if limα0(ecos(αn)eαm)=e2\displaystyle \lim_{\alpha \to 0} \left( \dfrac{e^{\cos(\alpha^n)}-e}{\alpha^m} \right)=-\frac{e}{2}

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