How to find limits of functions containing fractions | Calculus

In this calculus math example, we show the steps of how to solve the limit of a function that contains fractions inside of fractions as our variable is approaching a number by using factoring. 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 combine fractions in our numerator by first getting a common base for each. They are then combined to a single fraction. Our numerator is expanded by distributing and then simplified by combining like terms. We know what one of the factors will be because our numerator equaled zero. This leads us to factoring out a common factor and 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...

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