Notions of limits

 Before I introduce this lesson I'd like to make some considerations about math learning:

Nowadays many people turn to videos for learning. While this medium is great, written materials shouldn't put away. The written materials allow you to get an overview of what you  are going to learn and give you also the content in advance. You can choose which parts to learn first or which parts to drop depending on your interests. The most important thing also is you can review the materials as much as you can. If your reading skills are good you can learn a lot from written materials but for math there isn't a lot to read. You have to do the reading and memorize certain properties, formulas, etc. You have to practice a lot if you want to be proficient in math.

Here is the link of a detailed lesson on limits. Below is a guide  of the lesson  

Description of the lesson

This lesson starts by a definition of limits and shows you the three methods of limits using examples. Assignments consist of example assignment, practice assignment and review problems.  

 Outline

1. Objectives

The objectives of the lesson are given here. Read them to know the outcomes of the lesson. 

2. The Idea.

Here is given a conceptual definition of a limit. You can try to state this definition either in your own words without compromising the concept or verbatim for more accuracy. Now that you have a definition of limit you are going to learn  how to find the limit of a function using three methods: graph, table, algebra.

3. Methods for determining limits

a) The graph method

The graph method allows to find the limit of a function using its graph. An example is given that allows to know how to find the limit of a function using its graph. 

After reading the example and mastering the process of finding the limit the function from its graph, you should the two assignments: example assignment and practice assignment. Example assignment consists in doing the example. The practice example consists in doing an exercise that is not solved.

b) Table method

In this method you are going to use two tables to find a limit. You start by giving x some values to the left of the given value of x and you group the values of x and f(x) in a table. If you see from the table that f(x) gets closer and closer to a certain value when x gets closer and closer to the given value, that value represents the limit to the left. You do the same thing to the right of the given value of x to have a second table. If the limit to the right equals to the limit to the left, this limit represents the limit of the function.

After mastering the process of finding a limit of finding a limit using the table method, you should do the example assignment.

  

 Algebra method

This method is very simple but it involves some calculations to do. In this method you substitute x in the function to determine the limit. Here you find the limit directly. There is no limit to the left or the limit to the right to determine..

After mastering the solutions of the exercises that are examples, you do the assignment examples.

 Review problems

The review problems have problems Do the review problems involving the three methods.

Interested in learning more about limits get this free course Introduction to Calculus
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