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Question 240014
JEE Mathematics · Hard

Limits and Continuity: JEE Main MCQ

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JEE MainHardQuestion 240014

Question

lim(x→0) [x]/x (where [x] is the greatest integer function) is:
  1. A
    Limit does not exist
    Correct
  2. B
    0
  3. C
    1
  4. D
    −1

Correct answer

Limit does not exist

Explanation

Right limit: as x → 0⁺, [x] = 0, so [x]/x = 0/x → 0. Left limit: as x → 0⁻, [x] = −1, so [x]/x = −1/x → +∞. Limits differ, so the limit does not exist.

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