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AP Calculus AB: Introduction to Limits and Derivatives

This free math course explores how to define the limit of a function, 1- and 2-sided limits and the basis of derivation.

Publisher: ADU
This course describes the relevance of the limit of a function, and the concept of one-sided and two-sided limits in calculus. It looks at the relevance of the Sandwich theorem in calculating the limits of a function and the idea of continuity in differential calculus. By the end, you will be better informed on the mathematical idea of derivatives and the applications of derivatives in calculus.
AP Calculus AB: Introduction to Limits and Derivatives
  • Duration

    3-4 Hours
  • Students

  • Accreditation


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The study of limits and the closely related concept of continuity are an essential part of calculus. While the concept of a limit is easy to grasp, calculating limits can be demanding if the functions do not conform to customary patterns. In this course, the limit of a function, along with how to calculate limits, will be covered. The defined concepts and operations as they relate to limits and continuity will also be explained. In calculus, derivatives are used to measure the changes on a particular function. One of the important applications of calculus is in the analysis of the rate of change of events. This course discusses extensively the key ideas used in calculating the rate of change. You will study the behaviour of a function with limits and be taken through how to calculate the limits of functions using different methods.

Do you know that limits can be used to get the actual value of derivatives? Have you ever tried using graphs to find the limit of a function? It has been shown that this method can be incomplete. The course describes how to use algebraic properties of limits, also known as Limit laws, to estimate limits. It is important to have a sound grasp of Limit laws in order to derive theorems associated with advanced functions. This course discusses several types of functions and how to calculate the limit of a function as it approaches finite or infinite values. You will learn about continuous functions and how limits can be used to define continuity. Since limits form a fundamental building block for differential and integral calculus, it is important to learn how to navigate challenges presented by some limits problems. Generally, with more practice with different types of limits problems, it becomes easier to master calculus.

In searching for the limit of a function, it may be useful to study the behaviour of the function by means of a table of values. This course describes how to use rational functions in calculating the limit of a function. It describes how the process of calculating a limit can be simplified when the limiting process follows certain arithmetic operations. You will learn about the Sandwich theorem, which is a useful tool in calculating limits that do not yield to more ordinary forms of algebraic analysis. The material covers ways to calculate the limits of different types of functions. You will study how to evaluate limits and how these limits are applied in the study of calculus. There are some key areas in which limits occur in calculus. The study of areas under curves and volumes of solids is a major part of the study of integral calculus. Understanding limits is key to the understanding of this type of calculus. Are you interested in learning calculus for academic or professional reasons, then register for this course now.

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