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Recently I've found something very interesting concerning Taylor series.

It's a graphical representation of a second order error bound of the series.

Here is the link: http://www.karlscalculus.org/l8_4-1.html [Broken]

My question is: is it possible to represent higher order error bounds in a similar way?

For example: third order error term would have "3! = 6" in a denominator...

I know that Taylor series is based on Mean Value Theorem and I know the proof of it.

However it would become much clearer if it was possible to represent error bounds in a graphical way.

Have a nice weekend.

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# Taylor series error term - graphical representation

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