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The Average Rate of Change and Limits
This chapter introduces the concepts of Limits in the context of evaluating a Rate of Change. We begin by introducing the problem of change. How does a function change over time and in what ways can we quantify that? This leads to the introduction of the Limit. The rest of the chapter is dedicated to understanding what a Limit is, how to solve a Limit, and some applications of Limits. The chapter ends with the formal definition of a Limit, which is relatively advanced proof for this stage in mathematics.
By the end of this chapter, you should understand:
- What an Average Rate of Change is and how to solve for it
- What an Instantaneous Rate of Change is and how we aim to solve it
- The definition of a Limit
- The definition of Continuity
- Examples of Discontinuities
- How to evaluate a Limit using a variety of techniques
- How to formally prove a Limit
- Some applications of Limits
List of Topics in this Chapter:
- The Average Rate of Change
- The Instantaneous Rate of Change
- The Limit
- Limit Laws
- Limits, Graphically
- Continuity
- Evaluating Limits with Algebra
- Evaluating Trigonometric Limits
- The Squeeze Theorem
- Infinite Limits
- The Intermediate Value Theorem
- The Formal Definition of a Limit (Epsilon-Delta Proof)
Unit Daily Plan
Practice Problems
- The Average Rate of Change
- The Instantaneous Rate of Change
- The Limit
- Limit Laws
- Limits, Graphically
- Continuity
- Evaluating Limits with Algebra
- Evaluating Trigonometric Limits
- The Squeeze Theorem
- Infinite Limits
- The Intermediate Value Theorem
- The Formal Definition of a Limit (Epsilon-Delta Proof)
Sample Assessments
Solution Sets
- The Average Rate of Change
- The Instantaneous Rate of Change
- The Limit
- Limit Laws
- Limits, Graphically
- Continuity
- Evaluating Limits with Algebra
- Evaluating Trigonometric Limits
- The Squeeze Theorem
- Infinite Limits
- The Intermediate Value Theorem
- The Formal Definition of a Limit (Epsilon-Delta Proof)