Visualization of the Taylor Series

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Using 3blue1brown's animation code, I tried to code out the animation for the visualization for Taylor Series encountered in Calculus II.
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Why does is not align at the end? Should it be possible to do so, why not?

ianthehunter
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would you be able to add a version where the areas where the function and its taylor expansion are the same are highlighted per chance?

ballballballballballballball
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What software do you use to do this? It looks great

lorenzopapi