For each $x \in \mathbb{R}$, Let $[x]$ represent greatest integer function, then $\lim _{x \rightarrow 0^{-}} \frac{x([x]+|x|) \sin [x]}{|x|}$ is equal to

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Aicharya · Accepted Answer

$\begin{aligned} & \lim _{x ightarrow 0^{-}} \frac{x([x]+|x|) \sin [x]}{x} \ & 	ext { For } x ightarrow 0^{-},[x]=-1,|x|=-x \ 	herefore \quad & \lim _{x ightarrow 0^{-}} \frac{x(-1-x) \sin (-1)}{-x} \ & =\lim _{x ightarrow 0^{-}} \frac{-(1+x) \sin (1)}{1} \quad \ldots[x ightarrow 0, x 
eq 0] \ 	herefore & =-(1+0) \sin 1 \ & =-\sin 1\end{aligned}$

For each $x \in \mathbb{R}$, Let $[x]$ represent greatest integer function, then $\lim _{x \rightarrow…

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