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Help with Limits! (as x approaches a number)

Help with Limits! (as x approaches a number)

Author: Alex G
Description:

By the end of this packet you should be able to:
* Find the limit as x approaches a number using substitution
* Find the limit as x approaches a number using factoring followed by substitution
* Know when limits do not exist
* Examine limits on a grapher

This packet will take you through the steps of finding the limit as x approaches a number.

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Tutorial

Finding the Limit Through Substitution

The first thing you should always try is using substition to evaluate limits. This is an example of a limit that can be evaluated with substitution.

The Limit Does Not Exist

What it looks like when the limit does not exist.

Finding the Limit by Factoring (Example 1)

Sometimes substitution results in an indeterminant form. In that case, try factoring.

Finding Limit by Factoring (Example 2)

Indeterminant forms require more work. This video shows difference of two squares and using conjugate pairs to resolve an inderterminant form.

Looking at Limits on a Grapher

Examines the four limits above as a graph or a table.

Use LCD to Find Limits

Limit Does Not Exist (Vertical Asymptote)