`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_(xto-1) (1)/(sqrt(|x|-{-x})) (where {x} denotes the fractional part of x) is equal to

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

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

lim_(x->1) (x-1){x}. where {.) denotes the fractional part, is equal to:

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

If {x} denotes the fractional part of x, then lim_(xrarr1) (x sin {x})/(x-1) , is

lim_(x->0) {(1+x)^(2/x)} (where {.} denotes the fractional part of x (a) e^2−7 (b) e^2−8 (c) e^2−6 (d) none of these

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 (a) (-1/2,0) (b) (-1/2,2) (-1/2,2) (d) (1/2,oo)

lim_(x->oo)((x^3)/(3x^2-4)-(x^2)/(3x+2)) is equal to (a) does not exist (b) 1//3 (c) 0 (d) 2/9