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Online Textbook Chapters
Document
Examples when standard functions are or are not differentiable.
Prof. Daniel J. Kleitman
Differentiability (OT6.1)
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Document
Graphs of the types of discontinuities, including cusps, jump discontinuity, removable discontinuity, infinite discontinuity, and essential discontinuity.
Prof. Daniel J. Kleitman
Differentiability (OT6.1)
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Exam Questions
PDF - 2.2 MB
#Problem 1D-1 (page 3) to problem 1D-10 (page 4)
Ten questions which involve calculating one- and two-sided limits, identifying points of discontinuity, and making piecewise defined functions continuous and differentiable.
Prof. David Jerison
Limits and Continuity (CR-C)
Solution (PDF - 4.0 MB)# Pages 7 to 8
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PDF
Problem 5 (page 1)
Finding values where a piecewise defined function will be continuous and differentiable.
Prof. David Jerison
None
Solution (PDF)# Pages 3 to 4
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PDF
Problem 5 (page 1)
Finding values where a piecewise defined function will be differentiable.
Prof. David Jerison
None
Solution (PDF)# Page 1
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PDF
Problem 5 (page 2)
Finding values where a piecewise defined function will be differentiable.
Prof. David Jerison
None
Solution (PDF)# Page 2
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PDF
Problem 4 (page 1)
Finding the points where a piecewise-defined function will be differentiable.
Prof. David Jerison
None
Solution (PDF)# Page 1
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