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Teaching calculus with original historical sources has an important advantage. It is convenient to observe, how a new mathematical idea grows up in the mind of the author and it is convenient to make a similar image in the mind of students. It is possible to watch causes, which lead to the creations of the term. It is very important too, that students understand the way of thinking of the author,...
Many students have problems with solving tasks concerning the existence of the derivative of a function at a point. In this paper we discuss some of them.
Within the secondary school mathematics, the notion of an inverse function and its relationships to the original function does not attract much attention. In this article we deal with equations of the type f(x) = f-1(x) as a source of problems the solution of which leads to a better understanding of the notion of an inverse function. We make use of the PC programs Derive and WinPlot.
Professor Igor Kluvánek had developed a unique course of calculus (mathematical analysis) to teach students the differential and integral calculus. In the present paper, this concept is briefly outlined. The notion of derivative is introduced via continuity. The definition of integral given in this article applies an idea of Archimedes.
In the paper the authors analyse different shapes of an hourglass for the linearity of their graduation. We also assume that any hourglass (more precisely, each of the two congruent parts) has the shape of a solid of revolution and any cross section at height h of this hourglass depends on the base radius r, i.e. h = ƒ(r).
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