25 1A The value of In1 x for 1 SolutionNmax1000 numapporx2 a

Solution

Nmax=1000;
num_apporx=2;
approx=zeros(2,1);
approx(1)=-0.5;
approx(2)=0.5;
solution=zeros(Nmax,2,num_apporx);
%
for k=1:num_apporx
true=log(approx(k)+1); % true value
partial_sum=0; %resets partial sum variable
for i=1:Nmax
x=approx(k);
partial_sum=partial_sum+(-1)^(i-1)*x^(i)/i;
error=abs((true-partial_sum)/true);
solution(i,1,k)=i;
solution(i,2,k)=error;
end
end
loglog(solution(:,1,1),solution(:,2,1),\'b\',solution(:,1,2),solution(:,2,2
),\'r-\')
xlabel(\'Number of Terms\');
ylabel(\'Relative Error\');
legend(\'x=-0.5\',\'x=0.5\',2);