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JEE Advanced2017MathematicsLimitsActual

Let f x = 1 - x ( 1 + 1 - x ) | 1 - x | cos ⁡ 1 1 - x for x ≠ 1 , then

Options

  1. Alim x → 1 + ⁡ f ( x ) does not exist
  2. Blim x → 1 - ⁡ f ( x ) does not exist
  3. Clim x → 1 - ⁡ f x = 0
  4. Dlim x → 1 + ⁡ f x = 0

Correct answer

A. lim x → 1 + ⁡ f ( x ) does not exist

Step-by-step solution

f x = 1 - x cos ⁡ 1 1 - x , x < 1 - 1 + x cos ⁡ 1 1 - x , x > 1 lim x → 1 + ⁡ f x = does not exist ; (as cos t can take any value between -1 and 1, so oscillating.) lim x → 1 - ⁡ f x = 0 : (As cos t term varies between -1 and 1 for any value of t and is multiplied with zero)

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