AP Calculus AB Unit 1: Limits and Continuity
Flip your classroom and teach AP Calculus remotely! Unit 1 of the course focuses on limits and continuity. Informative videos introduce each lesson's topic, and the resource packets include worksheets, practice solutions, and two corrective assignments. In the first lesson, scholars learn about instantaneous rates of change by calculating average rates of change and then considering what would happen as the intervals become smaller and smaller. As the unit progresses, pupils learn the definition of limits and see how to determine a limit given a graph of a relation, learn the notation for one-sided limits and how to determine the value of a one-sided limit from graphs, how to find the limit of a function from a table of values, how to determine limits using algebraic properties, and how to use algebraic manipulation to determine limits. Other lessons teach pupils ways to algebraically determine the limit of a function at a specified value, connect multiple representations of limits, confirm continuity over an interval, and remove the discontinuity from rational functions. The Squeeze Theorem, infinite limits, and vertical asymptotes of rational functions are the topics of other lessons. The last lesson in the unit asks scholars to apply the Intermediate Value Theorem to a table of values to answer questions about the continuous function the table represents. Unit 1 ends with an end-of-unit review in which Individuals identify and classify discontinuities, investigate continuity at a point, evaluate limits at infinity, and determine horizontal asymptotes.