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JEE Main20199 Apr 2019Morning ShiftMathematicsContinuity and DifferentiabilityActual

If the function f defined on π 6 , π 3 by f x = 2 c o s x - 1 c o t x - 1 , x ≠ π 4 k , x = π 4 is continuous, then k is equal to

Options

  1. A1 2
  2. B1
  3. C2
  4. D1 2

Correct answer

A. 1 2

Step-by-step solution

∵   f x   is continuous at x = π 4 ∴   f π 4 = k = lim x → π 4 2 cos x - 1 cot x - 1 → 0 0 form Applying L' Hospital Rule k = l i m x → π 4 2 - sin x - cosec 2 x ⇒ k = 2 sin π 4 cosec 2 π 4 = 2 × 1 2 2 2 = 1 2 .

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