AP Calculus BC: Introduction to Limits and Differentiation
This free online course on examines limits, methods of differentiation and derivatives of trigonometric functions.Publisher: ADU
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AP Calculus BC: Introduction to limits and Differentiation is a free online course, specially prepared to take you through the concept of limits, continuity and derivatives. The study of limits and its closely related concept of continuity are an essential part are an essential part in the study of calculus. While the concept of a limit is usually pretty easy to grasp, calculating limits can be quite demanding if the functions do not conform to customary patterns. This course will take 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 will teach 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. An example of this is the piecewise-defined functions. It provides an opportunity to explore the relationship between one-sided and two-sided limits of a function. If you want to learn about sandwich theorem and its application, this course comes highly recommended. This course discusses the notion of horizontal and vertical asymptotes. Did you know that continuity is one of the most important concepts in calculus? Therefore, in our study of calculus, it is important to have a good understanding of this concept. This course 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.
Furthermore, if you want to learn about a variety of methods that can be used to differentiate both explicit and implicit functions, you should complete this course. This course explains in detail Pascal’s Triangle and the power rule. It states the Sum and Difference Rule, product rule as well as quotient rule. This course illustrates how to find the six trigonometric functions and differentiate a parametrized curve. It is often quite difficult or even impossible to solve for an explicit relationship between x and y when a functional relationship is implicitly defined. However, In this course, you will learn how to differentiate an implicitly defined function without needing to describe an explicit relationship between x and y. The learning contents in this course is crucial and will be of great interest to students, researchers, or anyone with an interest in excellent working knowledge of AP Calculus So, register for this course and start your next learning journey.Start Course Now
Limits and Application of Limits
Limits and Application of Limits - Learning Outcomes
Limits and Continuity
The Algebra of Limits
Sandwich or Squeeze Theorem
Limits and Application of Limits - Lesson Summary
Derivatives and Methods of Differentiation
Derivatives and Methods of Differentiation - Learning Outcomes
Definition of a Derivative and Notation
Methods of Differentiation
Derivatives of Trigonometric Functions
Composite Functions and the Chain Rule
Derivatives and Methods of Differentiation - Lesson Summary
Upon the successful completion of this course, you should be able to:
- Describe implicit differentiation.
- Recall how to differentiate a parametrized curve.
- Analyzes the process to find the derivatives of the six trigonometric functions.
- Summarize the power rule, keeping a multiplicative constant, product rule and the quotient rule.
- Discuss pascal’s triangle.
- State sandwich or squeeze theorem.
- List some of the application of limits.
- Outline the types of discontinuities.
- Recall how to solve for the algebra of continuous functions.
- Describe the relationship of limits to asymptotes.
- Recall how to find limits using tables or graphs.
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