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Some counterexamples for your calculus course
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Jürgen Appell
Published/Copyright:
January 18, 2011
Abstract
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.
Published Online: 2011-01-18
Published in Print: 2011-01-01
© by Oldenbourg Wissenschaftsverlag, Würzburg, Germany
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Articles in the same Issue
- Original Papers
- Some counterexamples for your calculus course
- Boundedness of some pseudo-differential operators on generalized Triebel–Lizorkin spaces
- Some topics related to universality of L-functions with an Euler product
- On the corkscrew condition for minimal sets
- Entire functions sharing values with their derivatives
- Expressions for two generalized Furdui series
- Differential polynomials which share a value with their derivative
- Toeplitz matrices, ergodicity and Fréchet spaces
- On algebraic selfsimilar solutions of the mean curvature flow
Keywords for this article
real functions;
continuity;
differentiability;
antidifferentiation;
bounded variation
Articles in the same Issue
- Original Papers
- Some counterexamples for your calculus course
- Boundedness of some pseudo-differential operators on generalized Triebel–Lizorkin spaces
- Some topics related to universality of L-functions with an Euler product
- On the corkscrew condition for minimal sets
- Entire functions sharing values with their derivatives
- Expressions for two generalized Furdui series
- Differential polynomials which share a value with their derivative
- Toeplitz matrices, ergodicity and Fréchet spaces
- On algebraic selfsimilar solutions of the mean curvature flow
