Taylor series for cos x

We know from Calculus that the Taylor expansion of cos x about x = 0

is given by

cosx = 1-x^2/2!+x^4/4!............

Write a Function or Script in MATLAB that will take N, x1, and x2

(respectively, the number of terms in this expansion and the interval of

comparison [x1, x2 ]) as inputs and will compare the actual function value

with its approximation. Use the interval [0; 6pi] and compare the actual

function with its expansion of 6 terms, 15 terms, and 30 terms (3 separate

plots). Limit your viewing window on the vertical axis to [-1:5 1:5].

please help me with this question

[KSSV]

What have you attempted for the question? If you google I am sure you will get the work around.

[Deleena Rebello]

function f=SineTaylorSeries(N,x1)
%This function takes two inputs N and x1. It compares the Taylor
%expansion of sine with (N+1) terms to the actual sine over
%the interval [-x1,x1].
x=-x1:0.1:x1;
SinePlot=zeros(size(x1));
for k=0:N
    SinePlot = SinePlot + (-1)^k*x.^(2*k+1)/factorial(2*k+1);
end
plot(x,SinePlot,'b')
hold on
plot(x,sin(x),'r+')
hold off
end

this a sample of sinetaylor series with only 2 input N and x1.

I want program for cos and 3 inputs N,x1,x2

Answer 1

[Rik]

There are a few edits you should make to your function:

% If you want a third input, just add it like this:
% (don't forget to edit the documentation)
function f=SineTaylorSeries(N,x1,x2)
%This function takes two inputs N and x1. It compares the Taylor
%expansion of sine with (N+1) terms to the actual sine over
%the interval [-x1,x1].
x=-x1:0.1:x1;
% ^^^
% I would suggest implementing this with linspace.
% This is also where you can put x2
SinePlot=zeros(size(x1));
%                   ^^
% Are you sure this should be x1? It looks like you should use x instead
for k=0:N
    SinePlot = SinePlot + (-1)^k*x.^(2*k+1)/factorial(2*k+1);
end
% The fact that you are creating a plot isn't documented.
% You should either remove it or document it
plot(x,SinePlot,'b')
hold on
plot(x,sin(x),'r+')
hold off

% You didn't define f anywhere. Is it supposed to be SinePlot? Or the
% handle to the figure with the plot? Something else still?
end

[Deleena Rebello]

the interval is between x1 and x2. So please make a update on that too

[Rik]

I suggested that you use linspace. Did you read the documentation? How do you think you could make sure the interval is between x1 and x2?