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

Question

displaystyle limx → 1 [x -1], where [.] is greatest integer function, is equal to (A) 1 (B) 2 (C) 0 (D) does not exists

Tardigrade Admin · Accepted Answer

Since, R.H.L = displaystyle limx → 1+ [x -1] = 0 and L.H.L. = displaystyle limx → 1- [x -1] = - 1 L.H.L ≠ R.H.L ∴ Limit of the given function does not exist.

Q. $x \to 1 lim [x - 1]$ , where [.] is greatest integer function, is equal to

1

2

0

does not exists

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

Q. x→1lim​[x−1], where [.] is greatest integer function, is equal to

1

2

0

does not exists

Since, R.H.L = x→1+lim​[x−1]=0 and L.H.L. = x→1−lim​[x−1]=−1 L.H.L = R.H.L ∴ Limit of the given function does not exist.

Q. $x \to 1 lim [x - 1]$ , where [.] is greatest integer function, is equal to

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