JEE-Advanced 2015 (25/40)

Calculus Level 2

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


The answer is 2.

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

Aqid Khatkhatay
Dec 21, 2016

Differentiate once Multiply divide by alpha raise to n Now alpha is zero so 2n-m should be zero to make the limit finite 2n-m=0 m/n=2

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