% x is a vector where x(i) = 10^(-i)
% this file shows that "f1(x) = 1 + O(h^2)"
% and "f2(x) = 0 + O(h^5)"

c1 = 7;
c2 = 3;

format long e
x = zeros(4,1);
for i = 1:4
    x(i) = 10^(-i);
end

% error of c1*f1(x)+c2*f2(x)-c1 record in a
% error of f1(c1*x)+f2(c2*x)-1 record in b
% According to the results , we can see that
% "c1*f1(x)+c2*f2(x) = c1 + O(h^2)"
%"f1(c1*x)+f2(c2*x) = 1 + O(h^2)"
a = zeros(4,1);
for j = 1:4
    a(j) = c1*f1(x(j))+c2*f2(x(j)) - c1*1;
end

b = zeros(4,1);
for j = 1:4
    b(j) = f1(c1*x(j))+f2(c2*x(j))-1;
end
a
b