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International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

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Volume 31, Issue 1


Some counterexamples for your calculus course

Jürgen Appell
Published Online: 2011-01-18 | DOI: https://doi.org/10.1524/anly.2011.1059


We discuss some examples and counterexamples that are used in first-year calculus courses to illustrate the interconnections between various function classes. Particular emphasis is put on the two-parameter family of functions (1.1) which provides an unexhaustable source of counterexamples.

Keywords: real functions; continuity; differentiability; antidifferentiation; bounded variation

About the article

* Correspondence address: Universität Würzburg, Institut für Mathematik, Am Hubland 9, 97074 Würzburg, Deutschland,

Published Online: 2011-01-18

Published in Print: 2011-01-01

Citation Information: Analysis International mathematical journal of analysis and its applications, Volume 31, Issue 1, Pages 1–12, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1524/anly.2011.1059.

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