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Many mathematical concepts in analysis (and in most other subfields of mathematics, except perhaps finite mathematics) involve "change" and some kind of limiting process. This makes them difficult to understand for many students both in secondary and tertiary education. Nowadays such limiting processes can be simulated using animations available in computer algebra packages running on all state of the art personal computers. In the implementation of such simulations it is necessary to avoid creating artifacts due to the finiteness of both soft- and hardware. The user should be able to choose the speed and other settings involved in the simulation, and should be able to create his own examples according to the same template. If this is achieved, the animations can greatly improve understanding of the concepts and ideas involved. Examples of this methodology are given using Mathematica.
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