Limit of Difference of two functions

In general as x -> a, f (x) -> l, then l is called limit of the function f (x) which is symbolically written as

The limiting process respects subtraction as long as the limits and functions under consideration are well defined. This is not a coincidence.

Let us check our formula for

Difference of limits with an example:

Let f and g be two functions such that both

exist. Then

(i) Limit of difference of two functions is difference of the limits of the functions, i.e.,

For Example: