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Tantalizing Taylor
This is two years of notes, sketches, and explanations / investigations of the Remainder Estimation Theorem (R.E.T. / LaGrange Error Bound), the convergence and divergence test, and other aspects of Infinite Series.
Part of this collection is a separate post, but I compiled them all together for my students' perusal and thought I would share the entire collection here.
Lastly, the two homework problems in the collection are there to highlight the concept of “Max f” or the “nth plus 1” derivative of f evaluated at c in the R.E.T., or LaGrange Error Bound. One of the problems uses a value for c that is at the end of the interval of approximation, and another uses a c value in the middle. This highlights the difference for the students so that they don't confuse this concept with the use of the endpoint in the (x-a)^(nth plus 1) which is always consistent.
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