18.01SC | Fall 2010 | Undergraduate

Single Variable Calculus

Part A: Definition and Basic Rules

Session 5: Discontinuity

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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

Clip 2: Removable Discontinuities

Clip 3: Infinite Discontinuities

Clip 4: Other (Ugly) Discontinuities

Clip 5: Differentiable Implies Continuous

Worked Example

Limits and Discontinuity

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Course Info

As Taught In
Fall 2010
Learning Resource Types
grading Exams with Solutions
notes Lecture Notes
theaters Lecture Videos
assignment_turned_in Problem Sets with Solutions
laptop_windows Simulations