Find `lim _(x to a ^(+))[(min (sin x, {x}))/(x-1)]` where `alpha` is root of equation `sin x+1=x` (here [.] represent greatest integer and {.} represent fractional part function)

FInd lim_(x->alpha^+) [(min (sin x, {x}))/(x-1)] where alpha is the root of the equation sinx+1 =x Here [.] represents greatest integer function and {.} represents fractional part function

lim_(xrarrc)f(x) does not exist for wher [.] represent greatest integer function {.} represent fractional part function

[2x]-2[x]=lambda where [.] represents greatest integer function and {.} represents fractional part of a real number then

The set of all values of x satisfying {x}=x[xx] " where " [xx] represents greatest integer function {xx} represents fractional part of x

Solve the following equation (where [*] denotes greatest integer function and {*} represent fractional part function ) [x^(2)]+2[x]=3x , 0 le x le 2 .

Find the solution of the equation [x] + {-x} = 2x, (where [*] and {*} represents greatest integer function and fractional part function respectively.

Let f(x) = [sin ^(4)x] then ( where [.] represents the greatest integer function ).

Draw a graph of f(x) = sin {x} , where {x} represents the greatest integer function.

The function f(x) = {x} sin (pi [x]) , where [.] denotes the greatest integer function and {.} is the fraction part function , is discontinuous at

Solve : x^(2) = {x} , where {x} represents the fractional part function.