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JEE Main2018MathematicsLimitsActual

For each t ∈ R , let t be the greatest integer less than or equal to t . Then lim x → 0 + x 1 x + 2 x + … + 15 x

Options

  1. Adoes not exist in   R
  2. Bis equal to 0
  3. Cis equal to 15
  4. Dis equal to 120

Correct answer

D. is equal to 120

Step-by-step solution

We know that 1 x − 1 < 1 x ≤ 1 x Hence, 1 + 2 + 3 . . . + 15 x − 15 < 1 x + 2 x + .... + 15 x ≤ 1 + 2 + ... + 15 x ⇒ lim x → 0 + x 1 x + 2 x + . ... + 15 x = 15 16 2 = 120

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