I need help formatting a table with disp and fprintf for a few Taylor Series outputs

syms x
f = 4*(-exp(-2*x)+exp(-x));
approx2 = taylortable(f,0,[0,0.5])


function approx2 = taylortable(f,x0,dom)
% set up the domain:
a = dom(1); b = dom(2);
if (x0 < a) || (x0 > b), x0 = a;
end
x = linspace(a,b,11)';
% 
% convert f and its derivatives to functions, and calculate their values at
% x = x0
F = matlabFunction(f); Fx0 = F(x0);
FP = matlabFunction(diff(f)); FPx0 = FP(x0);
FPP = matlabFunction(diff(f,2)); FPPx0 = FPP(x0);
FPPP = matlabFunction(diff(f,3)); FPPPx0 = FPPP(x0);
%
approx2 = zeros(11,3);
% find the exact and approximate values of f
for n = 1:11,
    approx2(n,1) = F(x(n));
    approx2(n,2) = Fx0 + (x(n)-x0)*FPx0;
    approx2(n,3) = approx2(n,2) + (((x(n)-x0)^2)/2)*FPPx0; 
    approx2(n,4) = approx2(n,3) + (((x(n)-x0)^3)/3)*FPPPx0;
end
disp(' x       Exact        Taylor-1       Taylor-2          Taylor-3')
fprintf('%5.3f,   %5.3f,        %5.3f,         %5.3f,            %5.3f\n', x, approx2(:,1), approx2(:,2), approx2(:,3), approx2(:,4))
end

The values for approx2 are not being taken by the disp or the fprintf commands

Answer 1

[Walter Roberson]

fprintf('%5.3f,   %5.3f,        %5.3f,         %5.3f,            %5.3f\n', [x(:), approx2].')

When you use fprintf(), it goes down columns in the input, using all of the first input (x) before it outputs any of the second variable, then goes down the columns of that, using all of that before outputing any of the next variable, and so on.

The trick I used here [x(:), approx2].' creates columns of data but then transposes them to become rows, so that the first entry in the temporary array is x(1), the second entry is approx2(1,1), the third is approx2(1,2) and so on.