This page provides the AB Calculus Manual for the classroom - all chapters of this manual are provided as free downloads! This section is a complete high school course for preparing students to tak e the AB Calculus exam. There is also a Review section that goes over the most common algebraic concepts that give students trouble. This manual can easily replace an expensive textbook. Teachers teach right from it and students write in it.
1.6 Determining Limits Using Algebraic Manipulation
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In the previous section, we evaluated limits by looking at graphs or by constructing a table of values. In this section, we establish laws for calculating limits and learn how to apply these laws. In the Student Project at the end of this section, you have the opportunity to apply these limit laws to derive the formula for the area of a circle by adapting a method devised by the Greek mathematician Archimedes. We begin by restating two useful limit results from the previous section. These two results, together with the limit laws, serve as a foundation for calculating many limits.