Taylor Maximum Error in the point 0.5

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

Answer 1

[Uday Pradhan]

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