Suppose $g$ is a function which has continuous derivatives, and that $g(8)=4, g'(8)=1$, $g''(8)=4$, $g'''(8)=5$.

(a) What is the Taylor polynomial of degree 2 for $g$ near $8$?
$P_2(x) =$

(b) What is the Taylor polynomial of degree 3 for $g$ near $8$?
$P_3(x) =$

(c) Use the two polynomials that you found in parts (a) and (b) to approximate $g(8.1)$.
With $P_2$, $g(8.1)\approx$
With $P_3$, $g(8.1)\approx$