A function f is said to be tend to a limit l at a point a of its domain, if when the independent variable x moves closure and closure to a, the dependent variable f(x) move closure to l.
In general, number l is said to be the limit of f(x) at x = a if for any arbitrarily chosen positive number ε however small but not zero, there exists a corresponding number δ greater than zero such that
|f(x) − l| < ε
for all values of x for which 0 < |x − a| < δ
means the absolute value of x − a without any regard to sign.