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Mathematics Question on limits and derivatives

lim⁡x→1[x−1] \displaystyle\lim_{x \to 1} [x -1], where [.] is greatest integer function, is equal to

A

1

B

2

C

0

D

does not exists

Answer

does not exists

Explanation

Solution

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