Friday, October 28, 2016

Notions of limits


Lesson: Introduction to the notion of limits

Objectives:

At the end of this lesson the learner should be able to:

1) Have an idea of what a limit is
2) Be able to calculate a limit using the graph, table and algebra method

This lesson is part of a series of lessons on the AP Calculus course I will be teaching throughout this blog. This lesson is the first lesson on Chapter I of the course. It is made of two parts. The first part is made of video lectures. The second part consists of the written lesson and the activities.

Video lectures

1) Introduction to the notion of limit

Here you'll have to watch this video that will introduce you the notion of limits. Here is the link: Introduction to the notion of limit

2) Methods for determining limits

The three methods for determining limits are: Graph, Table and Algebra method. You will have to watch three videos on the Graph method, two on the Table method and two on the Algebra method.

a) Graph method. 

Here are the links to watch the videos for this method:
Two-sided limits from graph
Limits examples Part I
Limits examples Part II

b) Table method

Here are the links to watch the links  for the Table method
Finding limits numerically with tables
Determine a limit numerically

c) Algebra method

In the Algebra method you are going to watch two videos.

1. In this video you are going to learn how to evaluate a limit using the substitution method and verifying the result using a graph. The notion of continuous functions is introduced to help to determine the limit. A continuous function is one that goes without interruption. The notion of continuity is introduced later in the Calculus course. Notice that the first function is a constant. As such the limit is a constant. This is one of the limit properties that will be introduced later. Since you don't know this property the limit is determined using a graph. The limits of the other 3 functions are calculated using the notion that if a function is continuous for a value x = c its limit is f(c). These 2 functions are continuous for any value of x. Therefore f(x) exists for any value of x and the direct substitution method is applied.

 Here is the link of the video to watch; Determining limit using direct substitution

2.. In this video you are going to use the three methods to evaluate a limit
2.1 Direct substitution
2.2 Factoring
2.3 Conjugation
Here is the link of the video to watch: How do you evaluate limits

In the next post I will introduce you to the written lesson that includes the assignments that you will have to do. You can also subscribe to the free Introductory Calculus course. If you want to get the complete Calculus course you can get it here (click on the highlighted word here)