Taylor's Theorem the Fast and Easy Way.
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At the end of proof you wrote the last equation which you got using generalized mean value theorem. Can someone explain how can I derive this equality?
Nice proof anyway :-)
0114mercury 6 months ago
@0114mercury Ah, great question. The generalized mean value theorem is used to find an explicit analytic form for the remainder term. We get what is called the Taylor Theorem WITH Remainder. The remainder is a big deal. It is used to confirm (or not) the convergence of the power series. In a rigorous sense the Taylor expansion is useless without the remainder. We have a proof of the GMVT in a previous video: What are Taylor Series? Part 2. Check it out...will add an annotation.
Mathview 6 months ago