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.


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

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