<![CDATA[How to evaluate derivative in a sequence cmd to create a list for taylor series]]>
https://help.geogebra.org/topic/how-to-evaluate-derivative-in-a-sequence-cmd-to-create-a-list-for-taylor-series
Thu, 22 Apr 2021 11:44:31 +0000Wed, 21 Apr 2021 15:19:10 +0000Zend_Feed<![CDATA[Have you tried this? https://wiki.geogebra.org/e...]]>
https://help.geogebra.org/topic/how-to-evaluate-derivative-in-a-sequence-cmd-to-create-a-list-for-taylor-series#comment-303664
Wed, 21 Apr 2021 20:53:04 +0000<![CDATA[That's a good question. I also couldn't find a simply way to do that (though I am not that familiar yet with the intricacies of GeoGebra). As a workaround you can use LeftSum: f(x) = x sin(x)
x_0 = 1
n = 7
Tf(x) = Sum(Sequence(LeftSum(Derivative(f, k), x_0, x_0 + 1, 1) / k! (x - x_0)^k, k, 0, n))
Btw, GeoGebra already has a TaylorPolynomial command.]]>
https://help.geogebra.org/topic/how-to-evaluate-derivative-in-a-sequence-cmd-to-create-a-list-for-taylor-series#comment-303670
Wed, 21 Apr 2021 21:33:19 +0000<![CDATA[Hi Michael, Yes, I am aware of the taylor polynomial. I became aware of it as I was looking at the forums earlier today. However while I can use this command, at this moment in time, I am more interested in learning the Syntax of Geogebra since that enables me to create more robust programs. I find that every time I look into things like this, I learn new and more efficient ways to create programs in geogebra. One of these days I'm going to challenge myself to generate a program to analyze waves similar to what is done by 3B1B in this video https://www.youtube.com/wat... I looked at some available Taylor series programs, and one of the more popular ones had used the spreadsheet to contain each iteration piece of the series, I thought this was interesting and thought it would be interesting to do this using a sequence cmd and generate a list.]]>
https://help.geogebra.org/topic/how-to-evaluate-derivative-in-a-sequence-cmd-to-create-a-list-for-taylor-series#comment-303686
Wed, 21 Apr 2021 23:02:00 +0000<![CDATA[LeftSum( <Function>, <Start x-Value>, <End x-Value>, <Number of Rectangles> )LeftSum(Derivative(f, k), x_o, x_o + 1, 1) So this is basically evaluating the area of a single rectangle that has a height equal to the kth derivative at x_o and a width of 1. That's a really interesting work around. I hope someone might be able to find something a bit more intuitive. I would have never thought of using this leftsum command in this manor. Cheers.]]>
https://help.geogebra.org/topic/how-to-evaluate-derivative-in-a-sequence-cmd-to-create-a-list-for-taylor-series#comment-303688
Wed, 21 Apr 2021 22:56:53 +0000<![CDATA[I found another workaround, but I am not sure if is is safe to use: LDerivatives = Sequence(Derivative(f, x, k), k, 0, n)
Tf(x) = Sum(Sequence(LDerivatives(k + 1, x_0) / k! (x - x_0)^k, k, 0, n)) The idea is to make a list of the derivatives and then use the short notation to access list elements, but with a second parameter x_0. Normally, two parameters (or more) are used to access elements of multidimensional lists (like matrices). The fact that this works for functions the way it does might be completely accidental, not a deliberate feature. Trying to do similar with the Element command (which also allows multiple parameters to access multidimensional lists) doesn't work.]]>
https://help.geogebra.org/topic/how-to-evaluate-derivative-in-a-sequence-cmd-to-create-a-list-for-taylor-series#comment-303708
Thu, 22 Apr 2021 11:44:32 +0000