Calculating Limits Using Algebra
  • Use of Direct Substitution
This idea states that this function is continuous at whatever value c may be

Some Basic Limits
- Let b and c be real numbers and let n be a positive integer.


Examples:







Properties of Limits
-Let b and c be real numbers, let n be a positive integer. and let f and g be functions with the following limits



1.Scalar multiple:

2. Sum or difference:



3. Product



4. Quotient


K cannot equal 0

5. Power



Example of a Limit of a Polynomial


The Limit of a Rational Function


Limits of Trigonometric Functions
1.
2.
3.
4.
5.
6.

Functions That Agree at All But One Point



Notice that if you apply the limit as is the denominator will equal 0 which is not allowed. You must factor out the numerator to solve this limit


Cancel out the (x-1) from the top and bottom by division and all you are left with is


Source--- Calculus with Analytic Geometry Eighth Edition. Houghton Mifflin Company, Boston/New York
example calculating limits using algebra