If `f(x)={((sin[x])/([x]), [x]!=0),(0,[x]=0):}`
where [.] denotes the greatest integer less than or equal to x then

If f(x) = {{:((sin[x])/([x]),[x] != 0),(0,[x] = 0):} , where [x] denotes the greatest integer less than or equal to x, then lim_(x to 0) equals

If f(x)={("sin"[x])/([x]) ,for [x]!=0, 0 ,for[x]=0,where [x] denotes the greatest integer less than or equal to x , then lim_(x→0)f(x) is (a) 1 (b) 0 (c) -1 (d) none of these

If f(x)={("sin"[x])/([x]),for[x]!=0 0,for[x]=0,w h e r e[x] denotes the greatest integer less than or equal to x , then ("lim")_(xvec0)f(x) is 1 (b) 0 (c) -1 (d) none of these

If f(x)={((tan^-1(x+[x]))/([x]-2x)[x]ne0,,),(0[x]=0,,):} where [x] denotes the greatest integer less than or equal to x, than lim_(xto0) f(x) is (a) (-1)/2 (b) 1 (c) (pi)/4 (d) Does not exist

If f(x)={((tan^-1(x+[x]))/([x]-2x)[x]ne0,,),(0[x]=0,,):} where [x] denotes the greatest integer less than or equal to x, than lim_(xrarr0) f(x) is

if f(x)=(sin[x])/([x]+1),x>0 and f(x)=((sin[x])/(2)[x])/([x]),x<0 and f(x)=k,x=0 where [x] denotes the greatest integer less than or equal to x=0, then in order that the continuous at x=0, the value of k is equal to