If `f(x) ={{:(sin[x]/[[x]]", "[x] ne 0),(" "0", "[x] ne 0):}` where, [x] denotes the greatest integer less than or equal to x, then ` lim_(x to 0) f(x) ` equalsA. 1B. 0C. `-1`D. None of these

If `f(x) ={{:(sin[x]/[[x]]", "[x] ne 0),(" "0", "[x] ne 0):}` where, [

1.	If `f(x) ={{:(sin[x]/[[x]]", "[x] ne 0),(" "0", "[x] ne 0):}` where, [x] denotes the greatest integer less than or equal to x, then ` lim_(x to 0) f(x) ` equalsA. 1B. 0C. `-1`D. None of these
Answer» Correct Answer - D Since, `f(x) = {{:((sin [x])/[[x]]", "[x] ne 0 ),("0, "[x] = 0):}` `rArr f(x) = {{:((sin [x])/[[x]]", "x inR-[0,1)),("0, "0 le x lt 1):}` At x = 0, RHL = ` underset(x to 0^(+)) lim 0 = 0` and LHL = `underset(x to 0^(-)) lim (sin [x])/[x] = underset( h to 0) lim (sin [0-h])/([0-h]) ` ` = underset( h to 0) lim (sin (-1))/(-1) = sin 1 ` `:. ` Limit does not exist.