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MHT CET20192 May 2019Morning ShiftMathematicsContinuity and DifferentiabilityActual

Which of the following function is not continuous at x = 0 ?

Options

  1. Af x = 1 + 2 x 1 x , x ≠ 0 = e 2 , x = 0
  2. Bf x = sin ⁡ x - cos ⁡ x , x ≠ 0 = - 1 , x = 0
  3. Cf x = e 1 x - 1 e 1 x + 1 , x ≠ 0 = - 1 , x = 0
  4. Df x = e 5 x - e 2 x sin ⁡ 3 x , x ≠ 0 = 1 , x = 0

Correct answer

C. f x = e 1 x - 1 e 1 x + 1 , x ≠ 0 = - 1 , x = 0

Step-by-step solution

Given f x e 1 / x - 1 e 1 / x + 1 x ≠ 0 - 1 x = 0 R.H.L. l i m x → 0 + 1 - e - 1 / x 1 + e - 1 / x = 1 ≠ f 0

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