% graphically demonstrates the squeeze theorem
% section 2.3 problem #32
%
%   f(x) <= g(x) <= h(x)
%   and as x->0,  f(x)->0 and h(x)->0
%
% using the squeeze theorem we get that 
%    as x->0 g(x)->0
%
x=-1:0.015:1;
f=-sqrt(x.^3+x.^2);
g=sqrt(x.^3+x.^2).*sin(pi./x);
h=sqrt(x.^3+x.^2);
plot(x,f,x,g,x,h)
legend('f(x)=-sqrt(x^3+x^2)','g(x)=sqrt(x^3+x^2)*sin(pi/x)','h(x)=sqrt(x^3+x^2)')