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MHT CET2019Evening ShiftMathematicsContinuity and DifferentiabilityActual

If function f x = x - x x , x < 0 = x + x x , x > 0 = 1 , x = 0 , then

Options

  1. Al i m x → 0 - f x does not exist
  2. Bl i m x → 0 + f x does not exist
  3. Cf x is continuous at x = 0
  4. Dl i m x → 0 - f x ≠ l i m x → 0 + f x

Correct answer

C. f x is continuous at x = 0

Step-by-step solution

Given function, f x = x - x x , x < 0 = x + x x , x > 0 , x = 0 Now, at x = 0 L H L = l i m x → 0 f x = l i m x → 0 x - x x l i m x → 0 x - - x x = l i m x → 0 x + 1 = 1 R H L = l i m x → 0 + f x = l i m x → 0 + x + x x = l i m x → 0 x + 1 = 1 f 0 = 1 ∴ l i m x → 0 - f x = l i m x → 0 f x = f 0 = 1 &#8658; f x is continuous at x = 0

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