JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

For each

x \in R

, let

[x]

be the greatest integer less than or equal to

x

. Then,

\lim \limits_ {x \rightarrow 1^{-}} \frac{x([x]+|x|) \sin [x]}{|x|}

is equal to

View answer and explanation

Correct option: A

-\sin 1

Option A (-

\sin 1

) is correct because after substituting the values for x approaching 1 from the left and simplifying, the limit evaluates to -

\sin 1

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