# Differentiability & Continuity

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## Online Textbook Chapters

#### Differentiability of Standard Functions

Document

Examples when standard functions are or are not differentiable.

Instructor: Prof. Daniel J. Kleitman
Prior Knowledge: Differentiability (OT6.1)

#### Examples of Non-Differentiable Behavior

Document

Graphs of the types of discontinuities, including cusps, jump discontinuity, removable discontinuity, infinite discontinuity, and essential discontinuity.

Instructor: Prof. Daniel J. Kleitman
Prior Knowledge: Differentiability (OT6.1)

## Exam Questions

#### Limits and Continuity

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.

Instructor: Prof. David Jerison
Prior Knowledge: Limits and Continuity (CR-C)

#### Piecewise Defined Functions

PDF
Problem 5 (page 1)

Finding values where a piecewise defined function will be continuous and differentiable.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Piecewise Defined Functions

PDF
Problem 5 (page 1)

Finding values where a piecewise defined function will be differentiable.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Piecewise Defined Functions

PDF
Problem 5 (page 2)

Finding values where a piecewise defined function will be differentiable.

Instructor: Prof. David Jerison
Prior Knowledge: None