Section 1.1

There are five types of limits we will be finding.

1.

means find the number that y is getting closer and closer to as x gets closer and closer to a from the right hand side. For example, to find

look at the values y assumes when x is 5.1, 5.01, 5.001, etc.

2.

means find the number that y is getting closer and closer to as x gets closer and closer to a from the left hand side. For example, to find

look at the values y assumes when x is 4.9, 4.99, 4.999, etc.

3.

means find the number that y is getting closer and closer to as x gets closer and closer to a from both sides. In order for this limit to exist, y must be approaching the same number from both sides. For example, to find

look at the values y assumes when x is –1.9, -1.99, -1.999, etc. and see if they are approaching the same number as the values y assumes when x is –2.1, -2.01, -2.001, etc.

Some things to keep in mind:

1. Remember that is not a number. If the y-coordinates are getting arbitrarily large, we write that the limit is , but this means the limit does not exist.

2. If y is approaching two different numbers, or oscillating back and forth between two numbers, or approaching from one side and - from the other side, we write d.n.e. as an abbreviation for “does not exist.”

3. When finding it does not matter what y equals when x equals a. The function f does not even have to be defined at a in order for the limit to exist.

If you missed class, you can watch my online movies. You must have QuickTime Player, a free download, installed on your computer.
The limit concept is movie 1 on this page.
Finding limits from graphs is movie 2 on this page.
One-sided limits is movie 1 on this page.

Some additional instruction on this topic:
What is a limit? from www.calculus-help.com