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  4. displaystyle lim x arrow 1[x-1], where [.] is greatest integer function, is equal to

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Q. $\displaystyle\lim _{x \rightarrow 1}[x-1]$, where $[.]$ is greatest integer function, is equal to

Limits and Derivatives

Solution:

Since, $RHL =\displaystyle \lim _{ x \rightarrow 1^{+}}[ x -1]=0$
and $LHL =\displaystyle \lim _{ x \rightarrow 1^{-}}[ x -1]=-1$
Hence, at $x =1$ limit does not exist.