`[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

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

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

Prove that [x]+[y] le [x+y] , where x=[x]+{x} and y=[y]+{y} [*] represents greatest integer function and {*} represents fractional part of x.

Prove that [x]+[y] le [x+y] , where x=[x]+{x} and y=[y]+{y} [*] represents greatest integer function and {*} represents fractional part of x.

Sum of all the solution of the equation ([x])/([x-2])-([x-2])/([x])=(8{x}+12)/([x-2][x]) is (where {*} denotes greatest integer function and {^(*)} represent fractional part function)

Solve the following equations (where [*] denotes greatest integer function and {*} represent fractional part function and sgn represents signum function)

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

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