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AP Calculus BC: Introduction to Limits and Differentiation

This online calculus course examines limits, methods of differentiation and derivatives of trigonometric functions.

Publisher: ADU
The concept of ‘limits’ is important to recognize the attributes of the real number system. This mathematics course discusses the evaluation of limits and their application. It also takes you through several methods used to differentiate between explicit and implicit functions. Many results in calculus require the functions to be continuous, therefore, it is important to understand continuous functions, which are covered in this course.
AP Calculus BC: Introduction to Limits and Differentiation
  • Duration

    4-5 Hours
  • Students

  • Accreditation


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This course has been specially prepared to take you through the concepts of limits, continuity and derivatives. The study of limits and 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. This course takes you through calculating both straightforward and more challenging limit problems. Since limits form a fundamental building block for both differential and integral calculus, it is important to learn how to navigate through issues presented by some limits problems. This course teaches you how to find limits through tables and graphs. You will learn about the limit theorems used to calculate the sum, difference, product and quotient of functions as well as for powers and roots. You will also learn about the limits of a trigonometric function. This course explores how to calculate a limit as it approaches infinite values.

Sometimes, we come across a function that requires more than one formula in order to obtain the given output, such as a piecewise-defined function. It provides an opportunity to explore the relationship between one-sided and two-sided limits of a function. If you want to learn about the sandwich (or squeeze) theorem and its application, this course comes highly recommended. It discusses the notion of horizontal and vertical asymptotes. Did you know that continuity is one of the most important concepts in calculus? The material defines continuity at a point and outlines the different types of discontinuities. It analyzes the slope of a curve at a point and the slope of the tangent to a curve. You will learn about derivatives and the formula for the derivative of a function.

If you want to learn about methods that can be used to differentiate both explicit and implicit functions, you should complete this course. It explains in detail Pascal’s Triangle and the power rule. It also expands on the sum, difference, product and quotient rules. The material illustrates how to find the six trigonometric functions and differentiate a parametrized curve. It is often difficult or even impossible to solve for an explicit relationship between x and y when a functional relationship is implicitly defined. However, you will learn how to differentiate an implicitly defined function without needing to describe an explicit relationship between x and y. Register for this AP Calculus course now and start your next learning journey today.

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