Question

2. The function fi(xo.h)= sin(xo +h)- sin(xo) can be transformed into another form. f2(xo,h), using the trigonometric formula + sin()-sin() =2cos sin 2 Thus, fi and f have the same values, in exact arithmetic, for any given argument values xo and h. (b) Suggest a formula that avoids cancellation errors for computing the approximation (f(xo +h)- f(xo))/h to the derivative of f(x) = sin(x ) at x xo. Write a MATLAB pro- gram that implements your formula and computes an approximation of f'(1.2), for h le-20,le-19,...,1

Answer 1

IF YOU HAVE ANY DOUBTS COMMENT BELOW I WILL BE TTHERE TO HELP YOU..ALL THE BEST..

AS FOR GIVEN DATA..

code:

clc
clear all
close all
x0=1.2;
h=-20:1:0;
h=10.^h;
f2=@(h) 2*cos((x0+h)/2).*sin((x0-h)/2);
v=f2(h);
fprintf('Values of h\t\tValues of f''(1.2)\n');
for i=1:length(v)
fprintf('%e\t%.17f\n',h(i),v(i));
end

I HOPE YOU UNDERSTAND..

PLS RATE THUMBS UP..ITS HELPS ME ALOT..

THANK YOU...!!