function [res] = equations(quadlimit)
% define the global paramters
global beta r 
global alpha n miu miuo lambda capa
% lambda = 0.75;
% alpha = 1.2;
% beta  = 0.5;
% r     = 0.01;
% n     = 10 ;
% 
% capa = 12;
% miu   = n.^(alpha-1)/(n.^(alpha-1)+2);
% miuo   = n.^(alpha-1)/(n.^(alpha-1)+1);
% the right of the certain inequation 
% rightvalue1 = r.^(3/2).*(1-lambda)./capa;
rightvalue1 = (capa).^(1./(alpha-1)).*(1-lambda);
% define the temp paramters 
a = 0;
b = quadlimit;
m = 800;
tol = 0.001;

% computer 
[R,quad,err,h]=romber('quadequ',a,b,m,tol);
quadvalue = quad;
% [R2,quad2,err2,h2]=romber('quadequo',a,b,m,tol);
% quadvalue2 = quad2;
leftvalue = (quad - lambda.*sqrt(pi)./2).*(quad + sqrt(pi).*(1-lambda)./(2.*(r.^(3/2))));

res=sum((leftvalue-rightvalue1).*(leftvalue-rightvalue1));