Session 5: Discontinuity

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Overview

Derivatives are defined in terms of limits of functions. Where those functions are not continuous, limits (and derivatives) may be undefined. This session discusses the different ways functions may be discontinuous and how differentiability is related to continuity.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Jump Discontinuities (00:03:00)

» Accompanying Notes (PDF)

From Lecture 2 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Removable Discontinuities (00:04:00)

» Accompanying Notes (PDF)

From Lecture 2 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 3: Infinite Discontinuities (00:06:00)

» Accompanying Notes (PDF)

From Lecture 2 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 4: Other (Ugly) Discontinuities (00:02:00)

» Accompanying Notes (PDF)

From Lecture 2 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 5: Differentiable Implies Continuous (00:08:00)

» Accompanying Notes (PDF)

From Lecture 2 of 18.01 Single Variable Calculus, Fall 2006

Worked Example

Limits and Discontinuity

 

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