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JEE Main2014MathematicsContinuity and DifferentiabilityActual

If the function f x = 2 + cos x - 1 π - x 2 , x ≠ π k , x = π is continuous at x = π , then k equals

Options

  1. A1 4
  2. B0
  3. C2
  4. D1 2

Correct answer

A. 1 4

Step-by-step solution

Given f x = 2 + cos x - 1 π - x 2 , x ≠ π k , x = π is continuous at x = π Hence, f π = lim x → π f x ⇒   k = lim x → π 2 + cos x - 1 π - x 2 Consider L . H . L . = lim x → π - 2 + cos x - 1 π - x 2 lim h → 0 2 + cos ( π - h ) - 1 π - π - h 2 Also, cos π - h = - cos   h ⇒   k = lim h → 0 2 - cos h - 1 h 2 ⇒   k = lim h → 0 2 - cos h - 1 h 2 × 2 - cos h + 1 2 - co

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