function hw4_sol
% problem 3 of sec 2.2
format long
h = 1./[ 4 8 16 32 ];
x = 1;

dF = [ 1/(2*sqrt(2)) -1/exp(1) 1 1/2 -pi ]

for fId = (1:5)
    fprintf(1,'Part-%d: dF(x=1)=%f\n\n',fId,dF(fId));
    fprintf(1,'\t\tinvH-value\t\t\t\tD1\t\t\t\tD2\t\t\t\tError1\t\t\t\tError\n',...
        dF(fId));
    fD1 = (fun( fId, x+h)-fun(fId,x))./h ;
    fD2 = (fun( fId, x+h)-fun(fId,x-h))./(2*h) ;
    disp([ 1./h; fD1; fD2; -(fD1-dF(fId)); ...
        -(fD2-dF(fId)); ]')
    pause%(1)
end

end

function val = fun( id, x )
switch id
    case 1,
        val = sqrt(x+1);
    case 2,
        val = exp(-x);
    case 3,
        val = log(x);
    case 4,
        val = atan(x);
    case 5,
        val = sin(pi*x);
end
end