Calculate the Taylor polynomials $T_2(x)$ and $T_3(x)$ centered at $x = 2$ for $f(x) = e^{-x}+e^{-2x}$.

$T_2(x)$ must be of the form $$A + B(x-2) + C(x-2)^2$$ where
$A$ = :
$B$ = : and
$C$ = :

$T_3(x)$ must be of the form $$D + E(x-2) + F(x-2)^2 + G(x-2)^3$$
where
$D$ = :
$E$ = :
$F$ = : and
$G$ = :