DANGER OF IMPROPER USE OF MATHEMATICAL RESULTS, FORMULAS AND SYMBOLS : LIMIT (CALCULUS)

Abstract

A lot of work has been done for the improvement of mathematics teaching in schools. Many textbooks in mathematics are also available in our country, where various mathematical problems have been worked out. But the study of the basic theory of mathematics involving theorems, formulas, symbols, etc., has not been so emphasised. Its consequence is very dangerous. It has been shown by the author [1, 2] with examples how fallacious results may be obtained while solving problems of algebra and trigonometry due to the lack of the basic concept in the theory. With the introduction of Calculus in the schools, it is necessary to point out similar fallacious results in Calculus, which may be obtained due to the improper use of these formulas, theorems, etc. In the present article which deals with the topic ‘Limit’, it will be shown with examples how the majority of students, while solving a problem, apply theorems and formulas of limit wrongly without considering the applicability of these results. It can be mentioned here that many textbooks in mathematics available in the market now-a-days also contain this type of conceptual errors. One of the purposes of this article is, therefore, to make the teachers and students aware of these errors.