For each $x \in R$, let $[x]$ be the greatest integer less than or equal to $x$. Then, $\mathop {\lim }\limits_{x \to {0^ - }} \frac{{x([x] + \left| x \right|)\sin [x]}}{{\left| x \right|}}$ is equal to

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 \to {0^ - }} \frac{{x([x] + \left| x \right|)\sin [x]}}{{\left| x \right|}}

is equal to

View answer and explanation

Correct option: C

- sin 1

Option C (- sin 1) is correct because it is the limit of the given expression as x approaches 0 from the left, obtained by substituting the greatest integer function and absolute value.

JEE MATHEMATICS MCQ: LIMITS

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