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JEE Main201911 Jan 2019Morning ShiftMathematicsLimitsActual

Let [ x ] denote the greatest integer less than or equal to X . Then : _ x 0 ( ² x )+(| x |- (x[x]))² x²

Options

  1. Adoes not exist
  2. Bequals
  3. Cequals +1
  4. Dequals 0

Correct answer

A. does not exist

Step-by-step solution

RHL is, _ x 0⁺ ( ² x )+(x-0)² x² = _ x 0⁺ ( ( ² x . x² +1 )=1+ And LHL is, _ x 0⁻ ( ² x )+(-x+ x)² x² = _ x 0⁻ ( ² x )+x²+ ² x-2 x x x² = +1+1-2= Since, LHL RHL Hence, limit does not exist.

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