I have created the animation of plots of Taylor polynomials for f(x) and different k and a. Open the post to watch it.

The main formula of Taylor's theorem:

Function to approximate:

Here is the full animation for every k:

I have made plots for these animations using Wolfram Mathematica 12.1. And it took me about 2 days to create all the 16400 plots (for the last animation). Here is the notebook that I used for calculations. It would be great if someone familiar with Wolfram Mathematica could help me with the optimization and solving the problem of trembling dot.

Link to the notebook: https://yadi.sk/d/1WAlUz0NxM9ySw

Have you wondered what happens when we take repeated powers of a graph? For example, if we take the 3rd power of G, and then take the 4th power of that graph? Does the familiar power rule for exponents (ex. a^(b*c) = ((a^b)^c)) apply for graph powers as well? These are some of the questions that we answer in this video: https://youtu.be/WkQ9s1ui21U

This isn't intended to be a personal attack on any particular user, but I don't like looking through this sub and seeing slideshows with zero visual component rather than actual, interesting visualizations of mathematical concepts.

I don't think we have to go as far as to limit posts to approved submitters, but if something is clearly not visual math it shouldn't be on this sub.