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JEE Advanced2015MathematicsLimitsActual

Let m and n be two positive integers greater than 1. If lim α → 0 ⁡ e c o s ⁡ ( α n ) - e α m = - e 2 then the value of m n is

Correct answer

0

Step-by-step solution

lim α → 0 ⁡ e cos ⁡ α n - e α m = - e 2 ⇒ Using L'Hospital's Rule lim α → 0 ⁡ e cos ⁡ α n ⋅ - sin ⁡ α n ⋅ n α n - 1 m ⋅ α m - 1 = - e 2 ⇒ m n = 2 .

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