Taylor series

Compute the Taylor polynomials $T_n$, $n=0,\dots,5$ of $f(x)=\sin x+\cos x$ at $x_0=0$. Solution: By Definition 5.3, we have to compute $f(x_0)$, $f’(x_0)$, $f^{(2)}(x_0)$, $f^{(3)}(x_0)$, $f^{(4)}(x_0)$, $f^{(5)}(x_0)$. It is not hard…