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MHT CET202611 April 2026Morning ShiftMathematicsLimitsActual

The value of _ x 3 [x] - 3 x - 3 , where [ ] denotes the greatest integer function, is.....

Options

  1. A1
  2. B0
  3. Cdoes not exist

Correct answer

3

Step-by-step solution

Evaluate the left-hand limit (LHL) and right-hand limit (RHL) at x = 3 . For LHL, let x 3⁻ . Then [x] = 2 . LHL = _ x 3⁻ [x] - 3 x - 3 = _ x 3⁻ 2 - 3 x - 3 = _ x 3⁻ -1 x - 3 = For RHL, let x 3⁺ . Then [x] = 3 . RHL = _ x 3⁺ [x] - 3 x - 3 = _ x 3⁺ 3 - 3 x - 3 = _ x 3⁺ 0 = 0 Since LHL RHL, the limit does not exist. Answer: does not exist

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