Formal Definition of a Limit

Let f be a function defined on an open interval containing c (except possibly c), and let L be a real number. The statement

lim{x right c}{f(x)}=L.

means that for each {epsilon} > 0 there exist delta>0 such that

0< delim{|}{x-c}{|} < delta then delim{|}{f(x)-L}{|} < epsilon .


Here is a video that demonstrates how to prove the limit is L using the delta-epsilon definition.