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Taylor Maximum Error in the point 0.5

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Duncan Weakley
Duncan Weakley il 10 Dic 2020
Risposto: Uday Pradhan il 16 Dic 2020
Hi There
I need to determine the maximum error which can be made with the taylor polynomial of g(x) = sinh(x^2) in the point x = 0.5
This is where c = 0;
For the third degree taylor polynomial.
I do not understand how to do this in matlab
could you please help me

Risposte (1)

Uday Pradhan
Uday Pradhan il 16 Dic 2020
Hi,
You can use the Symbolic Math toolbox to solve your issue as follows:
syms x;
f = sinh(x^2);
T = taylor(f); %finds the Taylor expansion around 0 till the fifth degree by default, to change order
% you can use 'Order' argument of taylor function
x = 0.5;
val = double(subs(T)); %find value of the Taylor polynomial at 0.5
val1 = sinh(x^2); %real value from the function
error = abs(val - val1); %find error
References: taylor, subs

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