If `f(x) = {{:(x+{x}+x sin {x}",","for",x ne 0),(0",","for",x = 0):}`, where {x} denotes the fractional part function, then

if f(x) ={x^(2)} , where {x} denotes the fractional part of x , then

If f(x)={x+{x}+x sin{x}, for x!=00, for x=0 where {x} denotes the fractional part function,then

Solve {x+1}-x^(2)+2x>0( where {.} denotes fractional part function)

if f(x) ={{:(2x-[x]+ xsin (x-[x]),,x ne 0) ,( 0,, x=0):} where [.] denotes the greatest integer function then

If f(x)={{:((sin(1+[x]))/([x]),"for" ,[x] ne 0),(0,"for",[x] =0):} where [x] denotes the greatest integer not exceeding x, then lim_(x to 0^(-))f(x)=

If f(x)={:(sin[x]","" ""for "[x]ne0),(0","" ""for "[x]=0):} where [x] denotes the greatest integer less than or equal to x. Then find lim_(xto0)f(x).