# 8. The Maclaurin series (a special case of the Taylor series that is discussed later in... 8. The Maclaurin series (a special case of the Taylor series that is discussed later in this class) allows us to express a differentiable, analytic function as an infinite degree polynomial. Here is the degree seven polynomial approximation of the sine: x3 x5 x? 3! 5! 7! + Use Matlab to generate a plot of sin(x) (solid blue line) and its polynomial approximation (dashed red line) for x = 0 to 31/2 and y from -1.5 to 2. Use the built-in factorial function in evaluating the polynomial expression. Employ only fplot, hold and axis commands to generate the plot.

Matlab code for the problem

clc; clear; % clearing the command window and workspace
% the 7th degree polymonial as matlab anonymous function
sine = @(x) x-x.^3/factorial(3)+x.^5./factorial(5)-x.^7./factorial(7);
x = [0 3*pi/2]; % x range
y = [-1.5 2]; % y range
fplot(@(x) sin(x),x,'b'); % plotting matlab sine function for x
hold on % hold the plot
fplot(sine,x,'r--'); % plotting the polynomial approximation of sine
axis tight
figure % next figure for y domain
fplot(@(x) sin(x),y,'b'); % plotting matlab sine function for y
hold on % holding the figure
fplot(sine,y,'r--'); % plotting the polynomial function for y
axis tight

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