AP Calculus

Definition of a Limit: L is the limit of f(x) as x approaches c, if and only if, for any positive number epsilon, no matter how small, there is a positive number delta such that if x is within delta units of c (but not equal to c), then f(x) is within epsilon units of L. (Math textbook, pg. 27)

L = Limit

E = epsilon

d = delta

When f(x)=L, x=c

When f(x)=L+E, x=c+d

When f(x)=L-E, x=c-d 

For more practice with limits, go to this link: http://www.slu.edu/classes/maymk/Applets/EpsilonDelta.html

Also:

F(x) = [x] is a greatest integer function, which creates the graph of a step function.

Homework for Monday, September 22

Exploration 2-2: The Definition of a Limit

Page 39 in textbook, problems 2 and 3

(Next class, in class: Concepts Problems, page 35 in textbook)

This entry was posted on Sunday, September 21st, 2008 at 11:25 pm and is filed under Class Notes and Assignments and You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.