We will continue learning about converging and diverging series. We will do problems using the integral test and the comparison test. We will also do an overview of series by identifying several specific types of series such as the geometric series, the harmonic series, the p-series, and alternating series.
Assignment
% problems from section 8.3 on the integral test.
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
We are moving through the work on series very nicely. Joshua is demonstrating a good understanding of this matrial.
We will define the integral test for determining if a series converges or diverges. We will use the test to do problems. We will also discuss the p-series.
Assignment
Five problems from section 8.3, due Friday.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
It was a very good session. We are making excellent progress in our study of calculus.
We will go over the assigned problems on series. We will do several more examples from involving series. We will begin section 8.3 on the integral test.
Assignment
None
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
Joshua has a good understanding of convergence and divergence of series. We will pursue this topic further using a variety of tests to determine if a series converges.
We will continuing working on infinite series, We will determine if a series converges or diverges. We will find the sum of the series if it converges. In addition, we will focus on geometric series and telescoping series.
Assignment
Six problems form section 8.2
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We are making steady progress in chapter 8. Joshua has a good understanding of series at this time.
We will do a few examples of limits of sequences to lead into the study of series. A series is the sum of the terms of a sequence. We will look for convergence or divergence of a series and identify several specific types of series. Examples will be done in class.
Assignment
None
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
We completed the work described in the outline. We will do more examples on Friday.
We will start by defining a sequence and identify terms of a sequence. We will use limits to determine if a sequence converges or diverges. We will find the value that a sequence converges to if it is a convergent sequence. We will look at graphs of sequences to determine convergence.
Assignment
none
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We got off to a good start on this topic. Joshua had a lot of basic knowledge of sequences that enabled us to jump right in to main objectives of this topic,
We will do one more example of integration by partial fractions. We will do multiple examples of improper integrals. This should complete chapter 7 in the text.
Assignment
None
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
We were able to complete multiple examples of improper integrals and one more example of partial fraction integration. We also looked at the standard normal distribution in terms of an improper integral.
We will do examples of finding limits using L'Hopital's rule. This will also enable us to review derivatives.
Lesson Outline
We will do a variety of examples of finding limits using L'Hopital's rule. We will emphasize the importance of the basic indeterminant forms necessary to be able to apply the rule. We will also approximate the limits numerically as a check of our results.
Assignment
none
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We had a productive session. We will be able to move on to improper integrals tomorrow.