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
» Clip 1: Jump Discontinuities (00:03:00)
From Lecture 2 of 18.01 Single Variable Calculus, Fall 2006
» Clip 2: Removable Discontinuities (00:04:00)
From Lecture 2 of 18.01 Single Variable Calculus, Fall 2006
» Clip 3: Infinite Discontinuities (00:06:00)
From Lecture 2 of 18.01 Single Variable Calculus, Fall 2006
» Clip 4: Other (Ugly) Discontinuities (00:02:00)
From Lecture 2 of 18.01 Single Variable Calculus, Fall 2006
» Clip 5: Differentiable Implies Continuous (00:08:00)
From Lecture 2 of 18.01 Single Variable Calculus, Fall 2006
Clip 5: Differentiable Implies Continuous
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Worked Example
Limits and Discontinuity