StellarA function has a discontinuity at a point if it is not continuous there. In Unit 1, the main types are removable discontinuities, jump discontinuities, and infinite discontinuities. A removable discontinuity happens when the limit exists, but the function is either undefined at the point or has the wrong value there. A jump discontinuity happens when the left-hand and right-hand limits both exist but are different. An infinite discontinuity happens when the function grows without bound near the point, often creating a vertical asymptote.
Back to Limits and Continuity
Lesson PreviewLesson 10 of 16 in this unit
1.10 Exploring Types of Discontinuities
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.
In this unit
16 lessons
- 1.1Introducing Calculus: Can Change Occur at an Instant?Preview lesson
- 1.2Defining Limits and Using Limit NotationPreview lesson
- 1.3Estimating Limit Values from GraphsPreview lesson
- 1.4Estimating Limit Values from TablesPreview lesson
- 1.5Determining Limits Using Algebraic Properties of LimitsPreview lesson
- 1.6Determining Limits Using Algebraic ManipulationPreview lesson
- 1.7Selecting Procedures for Determining LimitsPreview lesson
- 1.8Determining Limits Using the Squeeze TheoremPreview lesson
- 1.9Connecting Multiple Representations of LimitsPreview lesson
- 1.10Exploring Types of DiscontinuitiesThis lesson
- 1.11Defining Continuity at a PointPreview lesson
- 1.12Confirming Continuity over an IntervalPreview lesson
- 1.13Removing DiscontinuitiesPreview lesson
- 1.14Connecting Infinite Limits and Vertical AsymptotesPreview lesson
- 1.15Connecting Limits at Infinity and Horizontal AsymptotesPreview lesson
- 1.16Working with the Intermediate Value Theorem (IVT)Preview lesson
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