The road to Christmas break

First, here are the solutions for the Chapter 5 questions.

Secondly, here is the proposed syllabus up to Christmas Break.
12/17  5.3  Rules for Definite Integrals  HW p.290-291/1-17
12/21  5.3  Derivatives of Definite Integrals
                      HW p.291-293/19-37 odd,38,39,41,45-51 odd
12/22  5.4  Fundamental Theorem of Calculus  HW p.29
12/23  5.4  Fun Activity using Calculus

12/24 - 1/3 Christmas Break (Rest and Enjoy!)

Starting Ch 5 - The other half of Calculus

We have explored how to find the slope of any curve and many applications of knowing that rate of change. That was the first half of the Big Ideas of Calculus. Chapter 5 starts us on the path to the other Big Idea of Calculus - Integrals (definition to come soon!)

12/15 5.1 Estimating with Finite Sums (RAM) HW p.270/4-9,15,18,23-25,29,31-40
12/16 5.2 Riemann Sums -> Definite Integrals HW p.282-283/3-39 by 3's, 47-56

L'Hopital's Rule recap

The examples took all the time so let me recap when and how to use L'Hopital's Rule:

1.  Try to evaluate the limit. If the form is indeterminate, you may use L'Hopital's Rule

2.  Make sure the limit is written as a fraction (it must be in the 0/0 or infinity/infinity
     form).  You may have to rewrite the limit using logs or h = 1/x.

3.  Apply L'Hopital's Rule. Did you get a limit? Something undefined? You are done.

4.  Did you get another indeterminate form?  Apply L'Hopital's Rule again.

Remember that factoring, simplifying, applying other known limits and other limit techniques are always available.  Just because we are learning a new technique does not mean it is always the technique that can and should be used!