Taylor series Approximation of x*cos(x) at x = 2pi/3

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Thiago Augusto Borges Rodrigues 2020-1-9

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回答： Divya Yerraguntla 2020-1-13

I am trying to solve a how many terms of Macclaurin Serie are necessary to approximate f(2pi/3) into 10^-4 correct result. My results do not look right and I was not able to do the correct approximation. Can somebody help me?

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Thiago Augusto Borges Rodrigues 2020-1-9

Yes, I can show. First, I tried to find the error (code below). I manage to do it right, but I would not be able to find how many terms, considering the general taylor series formula.

>> syms x

>> f=inline('x*cos(x)');

>> T12 = taylor(f(x),x,0,'order',12);

>> T12x1 = subs(T12,x,2*pi/3);

>> eval (T12x1) - f(2*pi/3)

ans =

-3.041044905072177e-05

Thiago Augusto Borges Rodrigues 2020-1-12

Hey guys, maybe I did something wrong on my code. But, is there any other possiblity of help here? Thank you in advance.

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Answer 1

Divya Yerraguntla 2020-1-13

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Hi,

I'm assuming you want to know the number of terms in the T12 expression.

To do this you could use the function children which takes T12 as input and returns the terms of T12 in an array. You could find the number of terms in the array by using :

length(children(T12));

Hope it helps!