Properties of Limits
Read this section to learn about the properties of limits. Work through practice problems 1-6.
Limits of Some Very Nice Functions: Substitution
As you may have noticed in the previous example, for some functions it is possible to calculate the limit as
approaches a simply by substituting
into the function and then evaluating
, but sometimes this method does not work. The Substitution Theorem uses the following Two Easy Limits and the Main Limit Theorem to partially answer when such a substitution is valid.
Substitution Theorem For Polynomial and Rational Functions:
The Substitution Theorem says that we can calculate the limits of polynomials and rational functions by substituting as long as the substitution does not result in a division by zero.