# Write a function/script file that solves this problem on MATLAB

Write a function/script file that solves this problem on MATLAB

We will work with the function f(x) = e^-2x sin (x). (a) Find the 3rd degree Taylor polynomial for f (x) centered at x_0 = 0. Show your work. (b) Use this to approximate f(0.3). (c) What is the actual value of f(0.3)? How much (actual) error is present in our polynomial approximation at this point? (d) Plot f(x) and the Taylor polynomial on the same axes from about -1 to 1.

 Matlab Code clc clear vars syms x fx = exp(-2*x)*sin(x); taylor_poly = taylor(fx,x, 0, ‘Order’, 3); % Calculating taylor series fprintf(‘(a) %sn’, char(taylor_poly)); % Printing the series b = double(subs(taylor_poly, 0.3)); % Calculating the series for x = 0.3 fprintf(‘(b) f(0.3) = %fn’, b); c = double(subs(fx, 0.3)); % Calculating the actual value of f(0.3) fprintf(‘(c) Actual value of f(0.3) = %fn’, c); Actual_error = double(abs(b – c)); % error calculating fprintf(‘(c) Actual Error = %fn’, Actual_error); interval = [-1 : 0.1: 1]; fx_points = subs(fx, interval); taylor_points = subs(taylor_poly, interval); % Plotting the functions plot(fx_points, ‘k’, ‘LineWidth’, 1.5) hold on plot(taylor_points, ‘b’, ‘LineWidth’, 1.5) title(‘Plot of Function vs its Taylor series’); l = legend(‘f(x) = e^(-2x)sin(x)’, ‘Taylor Polynomial of f(x)’); set(l,’Location’,’southeast’)

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