MATLAB: Taylor series approximation of e^x at x =-20

Question

I'm trying to evaluate the Taylor polynomials for the function e^x at x = -20. My results do not look right and I don't know what's wrong with my for loop. Also, I can't seem to plot my data correctly with one being the approximate and the actual one on the same graph. Here's my code:

    n = 1;
    x = -20;
    %terms = 0;
    terms = zeros(1, n+1);
    for j = 0:1:n
        terms(j+1)=(x.^j)/factorial(j);
        %display(terms)

    end;
    %display(terms)
    termsSum = sum(terms);
    display(terms)
    display('The approximate estimate at x = -20')
    display(termsSum)
    %true value at x=-20
    display('TRUE VALUE')
    display(exp(x))
    %absolute error between the approximated and true value
    display('The error: ')
    t = exp(x)
    y = termsSum
    h = abs(t-y)
    display(h)
    %plot the approximation
    %plot(-22:0.001:-18,termsSum,'o')
    plot(terms,h, '*')

Answer 1

You're better off approximating exp(+20) with the Taylor series, and then taking the reciprocal of that.

    n = 50;
    x = -20;
    %terms = 0;
    terms = zeros(1, n+1);
    for j = 0:n
        terms(j+1)=(abs(x).^j)/factorial(j);
    end;
    termsSum = sum(terms);
    t = exp(x);
    y = termsSum.^sign(x);
    h = abs(t-y);

This avoids the numerical instability of summing over large terms with opposite signs. As for plotting, it's not clear to me what you're plotting things as a function of. n? x?