Limits


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  aδ

means the absolute value of  a  without any regard to sign.