clc;
clear all;
close all;

x=1.2;                                             %Setting the x value given in the notes. At which we are evalutating
h=logspace(-16,-2, 1000);                          %Logarithmically producing the start and end values with even intervals.
y=(0.5*h)*abs(-sin(x));                            %working out the second derivative of the function

f=zeros(1000);                                     %Creates a 1000x1000 zeros matrix

for i=1:1000                                       %for loop for 1000 itterations from i=1 to i=1000
    f(i)=abs(((sin(x+h(i))-sin(x))/h(i))-cos(x));  %This is the expression that was given in the lecture notes. Every itteration the value of h will go up by 1. (1 till 1000)
end

loglog(h,f,'k',h,y,'r')                            %Producing a logatithmic plot of the
xlabel('h')                                        %Labelling the x axis
ylabel('Discretization errors')                    %labelling the y axis
title('Round-off and discretization errors')       %titel for the graph