%EJEMPLO DE ALGORITMO INESTABLE!!
%ELABORADO POR PROF. MARLLINY MONSALVE

close all
clear all
clc

%======================================
%SECUENCIA QUE "CALCULA" EL AREA BAJO LA CURVA
n = 60;
y(1) = log(6)-log(5); %Valor inicial
for i=1:n;
    y(i+1) = (1/i)-5*y(i); %#ok<AGROW>
end
%======================================

n=[1 4 8 12 24 48 60];
tn = length(n);
X = 0:1e-4:1;
figure('Position',[300,300,650,550],'Name','ALGORITMO INESTABLE');
title('Grafica para f(x) = x^n/(x+5) en [0,1]','FontSize',13)
hold on


%GRAFICAS PARA VER EL AREA BAJO LA CURVA
pos=0.11;
for k=1:tn
    Y= (X.^n(k))./(X+5);
    h = plot(X,Y);
    col = [rand rand rand];
    
    set(h,'LineWidth',2,'color',col);
    etqs(1,k)=cellstr(strcat('n = ',num2str(n(k))));  %#ok<AGROW>
    legend('String',etqs);
    legend('Location','BestOutside');

    
    text(0.4,0.17,...
	['Observe al area bajo la curva'],...
	'HorizontalAlignment','center',... 
	'BackgroundColor',col,...
	'Margin',10);

       
    pos=pos - 0.01;
    text(1.01,pos,['y_{',num2str(n(k)),'}','= ',num2str(y(n(k)),'%0.5g')],'Margin',10);    
    disp('ENTER para continuar') 
    pause
end
text(0.4,0.15,...
	['SIEMPRE DISMINUYE!!'],...
	'HorizontalAlignment','center',... 
	'BackgroundColor',[0.5 0.5 0.9],...
	'Margin',10,'FontSize',11);

text(1.2,0.03,...
	['PERO y_n AUMENTA'],...
	'HorizontalAlignment','center',... 
	'BackgroundColor',[0.5 0.5 0.9],...
	'FontSize',11);