Scribe Notes 9/7/2010

UPDATE:
We now know that limits are a way to find the derivative of a function, that and . These formulas are a way of finding the derivative by finding its limit, which is what we did in class on 9/7/2010. So the purpose of finding the limit can be to tell what the derivative is. We also know now that at points where we found that the limit D.N.E. because of non-removable discontinuities (gaps), there is no derivative.

In assignment 1 of unit 2, problem 5 asks us to use the definition of the derivative to write a limit expression for . When we did this, we found that since the function is an absolute value, you have to split it into the positive portion and the negative one. We found that the positive and negative limits don't equal each other. Approaching from the negative side, the limit = -1, and from the positive side the limit = 1. Since they don't equal each other, the limit D.N.E.

Also, number 6 has a non-existent limit.

This site has a bunch of lessons on calculus, and the first 3 are about limits:
http://www.calculus-help.com/tutorials/

This site is talks about what limits are, and how to evaluate them:
http://www.sparknotes.com/math/precalc/continuityandlimits/section2.rhtml