Taylor_S

So for today's work, I think I need to become more clear about Taylor series

which can be used to estimate a function about a point, or actually define a

trigonometric function. These arose as the power of Calculus was starting to

be appreciated to 'backwards engineer' . Will be on my ever-appreciated Math is Fun

site, and their helpful problem sets.

https://www.mathsisfun.com/algebra/taylor-series.html

Asked Bing/Chatgpt how a calculator does operations on e:

                                                          

                                                               *     *     *

Taking the plunge on series, with the simplest I could find. Using

my python skills to generate results is turning out a bit wordy...

                                                                                          

                                                       

                                                                           

                                                      ...

Up to seven sound decimals on the Maclaurin expansion for e^x!

                                                                                  

Here's the fun part about this series. The very same series expansion is what defines e

to begin with, only with x set to 1. Put differently, we are computing e anew every time we

ask for e to some power...

                                                                         

                                                                            

                                                                            *     *     *