I tried to solve this quistion about

(find Taylor polynomials of order 3 near x=1 for f(x)=ln(x). I got the answer that is log(x) but whene I calclated it I got x-x^2/2+x^3/3)

I wrote

syms x;

f(x)=log(x)

t3=taylor(f,x,1,'order',4);

and I got the answer that is log(x)

MATLAB R2019b

[Walter Roberson]

f(x)=log(x)

That command has no semi-colon at the end of it, so MATLAB is going to display the result of f(x), which is going to be log(x)

t3=taylor(f,x,1,'order',4);

That command does have a semi-colon at the end of it, so MATLAB is not going to automatically display the result of the calculation. If you were to remove the semi-colon you would see the taylor approximation.

Answer 1

[David Hill]

What I got, which should be good for log(x) close to 1, is:

t3 = x - (x - 1)^2/2 + (x - 1)^3/3 - 1;