JEE Main 2019MathematicsLimitsMediumMCQ

JEE Main 2019 — Limits Question with Solution

JEE Main 2019 (09 Jan Shift 2)

Question

For each x∈R, let x be the greatest integer less than or equal to x. Then limx→0-xx+xsin⁡xx is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C-sin⁡1

Step-by-step explanation

=limx→0-⁡x x+xsin⁡xx

=limx→0-x-1-xsin⁡-1-x     x=-1,∀ x∈[-1,0)

=limx→0--1+xsin⁡1       sin-θ=-sinθ

=-sin⁡1.

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About this question

This is a previous-year question from JEE Main 2019, covering the Limits chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.