Approximate Value Using Taylor Polynomial

I have the following problem:

Use MATLAB to help you approximate f(5) using a 10th degree Taylor polynomial centered at

c = 4 for the function f(x) = sin2(x) cos(x).

I keep getting several different errors. The following is different methods I have tried with no luck. When I don't get an error, x is still in the answer. I am trying to find a value after it is evaluated. What can I do to solve this problem?

%1
syms x

f= (sin(x).^2).*(cos(x))

T = taylor(f,x,'ExpansionPoint',4,'Order',10)
%2
syms x
T = taylor((sin(x).^2).*(cos(x)),x,'ExpansionPoint',1)

%3
syms x
f =@(x) (sin(x).^2).*(cos(x))

T = taylor(f(5),'order',10)

Answer 1

[KSSV]

syms x 
f = (sin(x).^2).*(cos(x))

f = 

T = taylor(f,x,'order',10)

T = 

double(subs(T,5))

ans = -1.2435e+04

[codeconstructo]

Thank you. Spent 4 hours for it to be that simple. Nice

[Torsten]

syms x 
f = (sin(x).^2).*(cos(x))

f = 

T = simplify(taylor(f,x,'order',11,'ExpansionPoint',4))

T = 

fliplr(coeffs(T)).'

ans = 

double(subs(T,5))

ans = 0.2605

double(subs(f,x,5))

ans = 0.2608

Answer 2

[Rajeev]

You can first subsitute x in T using the 'subs' function and then use the 'double' to convert the answer to double precision type at the value x. Example:

This script returns a syms variable T,

syms x

f= (sin(x).^2).*(cos(x))

T = taylor(f,x,'ExpansionPoint',4,'Order',10)

substitute x with 5 as in T as given below:

sub_T = subs(T,x,5)

evaluate the value at 5 using the 'double' like:

ans = double(sub_T)

Refer to the documentation for more information:

subs: Evaluate Symbolic Expressions Using subs - MATLAB & Simulink (mathworks.com)

double: Double-precision arrays - MATLAB (mathworks.com)