Definition of a LimitSection 2.4

The Formal Definition of a Limit

provided given any

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!!!!!!!

lim ( )x a

f x L

0

0 ( )f x L 0 x a

This concept is not required for the AP test, but it required for the ACP curriculum.

Given any 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

0