This small paper contains some very-basic counter-examples in calculus. It is a suplementary resource intended to enhance the teaching and learning of a first-year university calculus course. The main part of the book contains incorrect statements form 5 topics found in introductory calculus courses: functions, limits, continuity, differential calculus and integral calculus. The most special thing which I get from this book is “picture-technique skill” to build counter-examples. This skill is so simple but require good imaginations and basic understanding of the meaning of definitions of elementary-level calculus. I think these easy counter-examples will give us “the first stable step” to get accustomed to building more complicated and significant both examples and counter-examples in other fields of mathematics.
https://hongnguyenqu...le-in-calculus/