Definition of a Limit
Section 2.4
f ( x)  L
 lim
x a


 0
provided given any   0

f ( x)  L  
0 xa 
The limit of f(x) as x approaches a is L
provided given any epsilon greater than zero
there exists a delta greater than zero such
that the absolute value of f(x)-L is less than
epsilon whenever zero is less than the
absolute value of x-a which is less than
delta!!!!!!!
The Formal Definition of a Limit

Given any   0 you must be able to find a 
that satisfies the problem.

 measures how close to f(x) is to its
limit.

The size of  depends on

This concept is not required for
the AP test, but it required for the
ACP curriculum.