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JEE Main20199 Apr 2019Evening ShiftMathematicsLimitsActual

If f x = x - x 4 ,   x ∈ R , where x denotes the greatest integer function, then:

Options

  1. Al i m x → 4 + f x exists but l i m x → 4 - f x does not exist
  2. Bf is continuous at x = 4
  3. Cl i m x → 4 - f x exists but l i m x → 4 + f x does not exist
  4. DBoth l i m x → 4 - f x and l i m x → 4 + f x exist but are not equal

Correct answer

B. f is continuous at x = 4

Step-by-step solution

R . H . L . = l i m x → 4 + x - x 4 = 4 - 1 = 3 L . H . L . = l i m x → 4 - x - x 4 = 3 - 0 = 3 f x = 4 - 1 = 3 L . H . L . = f 4 = R . H . L . Hence, given function is continuous at x = 4 .

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