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Taylor Maximum Error in the point 0.5

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Duncan Weakley
Duncan Weakley on 10 Dec 2020
Answered: Uday Pradhan on 16 Dec 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

Answers (1)

Uday Pradhan
Uday Pradhan on 16 Dec 2020
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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