Question

question should be done on Matlab

4) Find the derivative of sin(2x) at x = 0.8 rad and find the value of h where the error is minimum as compared to the true value i.e. actual value or accurate value. a) Use for loop b) Use element by element operation

Answer 1

`Hey,

Note: If you have any queries related to the answer please do comment. I would be very happy to resolve all your queries.

a)

clc

clear all

close all

format long

x=0.8;

h=logspace(-1,-20);

emin=100;

hN=1;

f=@(x) sin(2*x);

for i=1:length(h)

Dy=(f(x+h(i))-f(x-h(i)))/(2*h(i));

err=abs(Dy-2*cos(2*x));

if(err<emin)

hN=h(i);

emin=err;

end

end

disp('h at which error is min is');

disp(hN);

b)

clc

clear all

close all

format long

x=0.8;

h=logspace(-1,-20);

emin=100;

hN=1;

f=@(x) sin(2*x);

Dy=(f(x+h)-f(x-h))./(2*h);

err=abs(Dy-2*cos(2*x));

hN=h(err==min(err));

disp('h at which error is min is');

disp(hN);

Kindly revert for any queries

Thanks.