A function f(x) is said to tend to the limit l at x=a
if given element>0 there exists a number delta>0
such that ; /f(x)-l/< that element
whenever ; /x-a/<delta
In simple words , f(x) is said to tends to the
limit l at x=a
if f(x) tends to l as x approaches a
through values of x greater then a
as well as values of x smaller than a.
The limit l of f(x) at x=a denoted by
lim x-->a f(x)=l
It is clear from above that
f(x) tends to the limit l at x=a implies .
lim x-->a+0 f(x) = lim x-->a-0 f(x)
=lim x-->a f(x) = l
provided both the right-hand and left-hand limits exists for
If the domain of definition of f(x) is
[a, b] , then existence of
lim x-->a+0 f(x) does not arise .
Similarly the question of existence
lim x-->b+0 f(x) also does not arise .