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JEE Main 2019 · 9 Jan · Shift II

JEE Main 2019 Mathematics question on Limits Continuity and Differentiability

For each x∈Rx \in R, let [x][x] be the greatest integer less than or equal to xx. Then,
lim⁡x→0−x([x]+∣x∣)sin⁡[x]∣x∣\lim_{x \to 0^-} \frac{x([x] + |x|) \sin[x]}{|x|} is equal to
  1. A.
    0
  2. B.
    sin⁡1\sin 1
  3. C.
    −sin⁡1-\sin 1
  4. D.
    1
Show answer

Correct option: C

[JEE Main 2019 · 9 Jan · Shift II]

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