Question

determine the taylor series about point x (subscript)0=5 for the function x^2

Answer 1

\(x^2\) is a polynomial, so the taylor series will be finite, i.e. it will look like
\[a(x-5)^2+b(x-5)+c\]

Answer 2

put \(f(x)=a(x-5)^2+b(x-5)+c\) then \(f(5)=c\) and so \(c=25\)

Answer 3

then \(f'(x)=2a(x-5)+b\) and so \(f'(5)=b\) hence \(b=10\)

Answer 4

guess i am alone here ok