Let an Interval be denoted by (a-β , a+β) which is shown by the figure below:

and x∈ (a-β , a+β)

And let a function f(x) be defined at the Interval (a-β , a+β) .

Then we can also find the limit of  function f(x) as,

Left hand Limit of a Function:

In the above  case the limit of f(x) when “x” approaches “a” from the left hand side of the interval is known as the left hand limit of f(x).

and is denoted by:

Right hand Limit of a Function:

Similarly,

the limit of f(x) when “x” approaches “a” from the right hand side of the interval is known as the right hand limit of f(x) and is denoted by: