f = chebfun( '(pi*x/0.01)/sinh(pi*x/0.01)', [-1,1] );
%f = 
%   chebfun column (1 smooth piece)
%       interval          length    endpoint values   
%(       -1,        1)     3441   2.3e-134  2.3e-134   
%vertical scale =   1 
figure(1),plot( f, 'k' )
t = linspace(-1,1,2012);
figure(2),semilogy( t, abs(sinh(pi*t/0.01).*f(t)*0.01./t/pi - 1 ), 'k' ),xlabel('x'),ylabel('relative error')
figure(3),semilogy( t, abs( f(t) - pi/0.01*t./sinh(pi*t/0.01) ), 'k' );
xlabel('x','fontsize',16);
ylabel('absolute error','fontsize',16);
set(gca,'fontsize',16);
axis([-1,1,10E-20,10E-14]);
figure(4),plot( roots(f,'complex'), 'ko' )
figure(5),plot( roots(1.0./f, 'complex' ), 'ko' ) % Fails.
