Evaluate the explicit form of the Taylor polynomial of degree 2n-1 for arctan(x) with the point of approximation 0

Write a Matlab code to evaluate the explicit form of the Taylor polynomial of degree 2n-1 for arctan(x) and the point of approximation 0.

So I tried to do this:

function value = polyeval(x, coeff);

n = length(coeff)

value = coeff(n)*taylor(arctan(x))

for i = n-1:-1:1

value = coeff(i) + x.*value;

end

But the teacher marked it as wrong. What would have been the correct way?

Answer 1

[Walter Roberson]

You tried to take the arctan of the polynomial degree, rather than the arctan of x.

In MATLAB, arctan is written as atan() or atan2()

MATLAB does not permit implicit multiplication, not anywhere . 2n is invalid MATLAB syntax in all cases: you need to supply a multiplication operator.

Example use of taylor:

syms x x0
f = sin(x).^2 - cos(x).^2

f = 

taylor(f, x, x0, 'order', 5)

ans = 

taylor(f, x, x0, 'order', 6)

ans = 

taylor(f, x, x0, 'order', 7)

ans = 

Your teacher expects you to figure out what the (2*n-1)'st term is of the taylor polynomial of arctan

[N/A]

How about this?

x = 1;

y = 0;

for i = 1:100

     y = y + (-1)^(i-1) * x^(2*i-1) / (2*i-1);

end

[Walter Roberson]

That might help . But the expected outcome is code that calculates one particular term, not code that calculates 100 terms.

[N/A]

So then just this? I just get rid of the for loop?

x = 1;

y = 0;

y = y + (-1)^(i-1) * x^(2*i-1) / (2*i-1);

[Torsten]

Can you take it from here ?

syms x
n = 4;
f = atan(x);
p = taylor(f,x,'ExpansionPoint',0,'Order',2*n)

p =