`lim _(xto 1 ^(-)) (e ^({x}) - {x} -1)/( {x}^(2))` equal, where {.} is fractional part function and I is aan integer, to :

Consider the function f (x)={{:(max (x, (1)/(x))",", If x ne0),(min (x, (1)/(x)),),(1"," , if x=0):}, then lim _(xto 0^(-)) {f(x)} + lim _(xto 1 ^(-)) {f (x)}+ lim _(x to 1 ^(-)) [f (x)]= (where {.} denotes fraction part function and [.] denotes greatest integer function)

lim_(x rarr1)({x})^((1)/(n pi x)) ,where {.} denotes the fractional part function

lim_(x rarr[a])(e^(x)-{x}-1)/({x}^(2)) Where {x} denotes the fractional part of x and [x] denotes the integral part of a.

lim_(x rarr2^(+))((2{x}-4)/([x]-3)) is equal to,where {.} and [.] represents fractional part of x and greatest integer function

The value of lim_(xto0)((tan({x}-1))sin{x})/({x}({x}-1) is where {x} denotes the fractional part function

The value of lim_(xto0)((tan({x}-1))sin{x})/({x}({x}-1) is where {x} denotes the fractional part function

Evaluate: ("lim")_(xto1)("xsin"{x})/({x-1}) if exists, where {x} is the fractional part of xdot

If lim _(x to c ^(-)) {ln x} and lim _(xto c ^(+)) {ln x} exist finitely but they are not equal (where {.} denotes fractional part function), then:

If lim _(x to c ^(-)) {ln x} and lim _(xto c ^(+)) {ln x} exist finitely but they are not equal (where {.} denotes fractional part function), then: