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

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

Limits and Derivatives

Solution:

Since, R.H.L = $ \displaystyle\lim_{x \to 1^+} [x -1] = 0$ and L.H.L. = $ \displaystyle\lim_{x \to 1^-} [x -1] = - 1$
L.H.L $\neq$ R.H.L
$\therefore $ Limit of the given function does not exist.