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1.1 Introducing Calculus: Can Change Occur at an Instant?

Part of Limits and Continuity in AP® Calculus BC. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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Average Rate of Change

In Unit 1.1 of AP Calculus AB/BC, you start by thinking about how a quantity changes over an interval. The average rate of change tells you how much a function changes between two inputs. It is calculated using:

f(b)−f(a)b−a\frac{f(b) - f(a)}{b - a}

This represents the slope of the line connecting two points on the graph. If the function represents position over time, then this value is the average velocity. It does not tell you what is happening at a specific moment, only over the entire interval.

In this unit

16 lessons

  1. 1.1Introducing Calculus: Can Change Occur at an Instant?This lesson
  2. 1.2Defining Limits and Using Limit NotationPreview lesson
  3. 1.3Estimating Limit Values from GraphsPreview lesson
  4. 1.4Estimating Limit Values from TablesPreview lesson
  5. 1.5Determining Limits Using Algebraic Properties of LimitsPreview lesson
  6. 1.6Determining Limits Using Algebraic ManipulationPreview lesson
  7. 1.7Selecting Procedures for Determining LimitsPreview lesson
  8. 1.8Determining Limits Using the Squeeze TheoremPreview lesson
  9. 1.9Connecting Multiple Representations of LimitsPreview lesson
  10. 1.10Exploring Types of DiscontinuitiesPreview lesson
  11. 1.11Defining Continuity at a PointPreview lesson
  12. 1.12Confirming Continuity over an IntervalPreview lesson
  13. 1.13Removing DiscontinuitiesPreview lesson
  14. 1.14Connecting Infinite Limits and Vertical AsymptotesPreview lesson
  15. 1.15Connecting Limits at Infinity and Horizontal AsymptotesPreview lesson
  16. 1.16Working with the Intermediate Value Theorem (IVT)Preview lesson

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