How to find limits using Synthetic Division to factor | Calculus

In this calculus math example, we show how to solve the limit of a rational function as our variable is approaching a number by using synthetic division to help us factor. The first step is to evaluate the expression at the number we are approaching. When we find that we get 0/0, we know to continue the problem. If it had been anything else we could have stopped with either a number or does not exist (DNE) as out answer. To continue, we want to factor the numerator. We know what one of the factors will be because our numerator equaled zero but finding the other is difficult because we have a third degree polynomial. To help us factor, we go through the steps to use synthetic division to find the quotient when our polynomial is divided by our known factor. After we have factored, the result is reduced to lowest terms. (Because we are taking a limit, we are allowed to do this.) Finally, we evaluate the remaining expression by replacing our variable with the value it is approaching from the limit and simplify completely. This video contains examples that are from Business Calculus, 1st ed, by Calaway, Hoffman, Lippman. from the Open Course Library, remixed from Dale Hoffman's Contemporary Calculus text. It was extended by David Lippman to add several additional topics. The text is licensed under the Creative Commons Attribution license. http://creativecommons.org/licenses/b... how to solve limits calculus limits of functions calculus limits and derivatives class 11