Abstract
When teaching function analysis, as part of college calculus, many of the same calculations repeat themselves, over and over again. These calculations are for proving limits (their existance and values, or perhaps the lack thereof), finding minima and maxima, determining continuity and differentiability at specific points, or for ranges, etc. We also present to our students, the summary of the analyses, in the form of detailed, annotated plots. We present the automation of function analysis, for teaching first-semester college calculus. The relevant Mathematica functions (and their options) are demonstrated, in a step-by-step fashion and discussed at length. The application of these functions, to the calculus material, and the pitfalls that can arise, are discussed. In addition to the automated results for limits, extrema, continuity, differentiability, etc., we also show how plotting can be achieved, including all of the analyses learned.
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Acknowledgements
The author wishes to thank Dr. Avi Naiman for many interesting correspondences, and helpful comments on the paper.
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Naiman, A.E. Automated Function Analysis for Calculus. Math.Comput.Sci. 13, 195–204 (2019). https://doi.org/10.1007/s11786-018-0358-0
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DOI: https://doi.org/10.1007/s11786-018-0358-0