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BITSAT2014MathematicsLimitsActual

_ x 0 ( cosec x)^ 1 / x is equal to :

Options

  1. A0
  2. B1
  3. C1 e
  4. DNone of these

Correct answer

C. 1 e

Step-by-step solution

Let y= _ x 0 ( cosec x)^ 1 / x Taking on both sides, we get y= _ x 0 cosec x x [ . form ]= _ x 0 - x 1 / x (ByL' Hospital rule) =- _ x 0 x x ( x= 1 x ) y=-1 y=e⁻¹= 1 e Hence, required limit = 1 e

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