Online College Courses for Credit

Help with Limits! (as x approaches a number)

Help with Limits! (as x approaches a number)

Author: Alex G

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.

See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

Begin Free Trial
No credit card required

46 Sophia partners guarantee credit transfer.

299 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 33 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.


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)