`lim_(x->-1)1/(sqrt(|x|-{-x}))(w h e r e{x}` denotes the fractional part of `(x)`) is equal to (a)does not exist (b) `1` (c)`oo` (d) `1/2`

lim_(x to 0) {(1+x)^((2)/(x))} (where {.} denotes the fractional part of x) is equal to

lim_(x->oo ){(e^x+pi^x)^(1/x)}= where {.} denotes the fractional part of x is equal to

Let f(x)=sqrt(|x|-{x})(w h e r e{dot} denotes the fractional part of (x)a n dX , Y are its domain and range, respectively). Then (a) X in (-oo,1/2) and Y in (1/2,oo) (b) X in (-oo in ,1/2)uu[0,oo)a n dY in (1/2,oo) (c) X in (-oo,-1/2)uu[0,oo)a n dY in [0,oo) (d) none of these

If f^(prime)(x)=|x|-{x}, where {x} denotes the fractional part of x , then f(x) is decreasing in (-1/2,0) (b) (-1/2,2) (-1/2,2) (d) (1/2,oo)

("lim")_(xvec1)(xsin(x-[x]))/(x-1),w h e r e[dot] denotes the greatest integer function is equal to (a) 0 (b) -1 (c) not exist (d) none of these

lim_(x->0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the greatest integer function). (a) -1 (b) 1 (c) 0 (d) does not exist

lim x→(2^+) { x } sin( x−2 ) /( x−2)^2 = (where [.] denotes the fractional part function) a. 0 b. 2 c. 1 d. does not exist

Find the domain and range of f(x)=log{x},w h e r e{} represents the fractional part function).

("lim")_(xvec1)[cos e c(pix)/2]^(1/((1-x)))(w h e r e[dot]r e p r e s e n t st h e gif is e q u a l to (a) 0 (b) 1 (c) oo (d) does not exist

For x in R , lim_(xrarroo)((x-3)/(x+2))^x is equal to (a) e (b) e^(-1) (c) e^(-5) (d) e^5