Untitled

% Power Series Approximation of e^x
taylor_exp = @(x, n) sum(arrayfun(@(k) x.^k ./ factorial(k), 0:n));
x = -2:0.1:2; % Define range
n_terms = [2, 5, 10, 20]; % Number of terms to compare
figure;
hold on;
for n = n_terms
y_approx = arrayfun(@(x) taylor_exp(x, n), x);
plot(x, y_approx, 'DisplayName', sprintf('%d terms', n));
end
plot(x, exp(x), 'k', 'LineWidth', 2, 'DisplayName', 'e^x');
legend;
title('Power Series Approximation of e^x');
xlabel('x'); ylabel('f(x)');
grid on;
hold off;
% Compute and Plot Error
figure;
hold on;
for n = n_terms
y_approx = arrayfun(@(x) taylor_exp(x, n), x);
error = abs(exp(x) - y_approx);
plot(x, error, 'DisplayName', sprintf('%d terms', n));
end
title('Error in Power Series Approximation of e^x');
xlabel('x'); ylabel('Error');
legend;
grid on;
hold off;