The value of   is equal to?

Where {x} denote the fractional part of x.

Concept:

Greatest Integer Function: Greatest Integer Function [x] indicates an integral part of the real number x which is a nearest and smaller integer to x. It is also known as floor of x

• In general, If n ≤ x ≤ n+1 Then [x] = n   (n ∈ Integer)
• Means if x lies in [n, n+1) then the Greatest Integer Function of x will be n.

Example:

Fractional part of x: fractional part will always be non-negative.

• It is denoted by {x}
• {x} = x - [x]

Existence of Limit:

 is exists if  and  exist and 

Calculation:

To Find: Value of 

As we know {x} = x - [x]

RHL = 

If x → 0⁺ then [x] = 0

RHL =         [Form (0/0)]

Apply L-Hospital Rule,

RHL = 1

LHL = 

If x → 0^- then [x] = -1

RHL ≠ LHL

So, the limit doesn't exist.