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

Question

For each x$ \in $R, let [x] be the greatest integer less than or equal to x.

Then $\mathop {\lim }\limits_{x \to {0^ - }} \,\,{{x\left( {\left[ x \right] + \left| x \right|} \right)\sin \left[ x \right]} \over {\left| x \right|}}$ is equal to :

$-$ sin 1

sin 1

Solution

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