Round off errors

• figure(1);
   x = [-7/2 -3 -5/2 -2 -7/4 -6/4 -5/4 -1 -7/8 -6/8 -5/8 -1/2 0  1/2 5/8 6/8 7/8 1 5/4 6/4 7/4 2 5/2 3 7/2]
  Y=ones(1,length(X))
    plot(X,Y,'ro','MarkerFaceColor', 'r', 'MarkerSize', 8);
  drawnow
  

• x1=[1:1e5];
  x2=[1e5:-1:1];
  y1=1./x1;y2=1./x2;
  S1=sum(y1);S2=sum(y2);format long;
  S1
  S2
  

• k=[-18:.01:-3];
  
  x=10.^k;
  
  a=((exp(x)-1)./x);plot(a);
  
  b=((exp(x)-1)./(log(exp(x))));
  
  plot(k,a,r');hold on
  
  plot(k,b,'b');hold on
  

•   x=2;k=[-20:.3:4];d=10.^k;
    e=log10(abs(cos(x)- (sin(x+d)-sin(x))./d));
    plot(k,e,'ro');
  

• x = [-5e-16:1e-18:5e-16]; y = (( 1- (1-x))./x);plot(x,y,'or')