Suppose $is$ a function which has continuous derivatives, and that $g(5)=-5,g(5)=4,g(5)=-2,g(5)=3$

$(a)$ What $is$ the Taylor polynomial $of$ degree $2$ for $g$ near $5?$

$p_2(x)=$

$(b)$ What $is$ the Taylor polynomial $of$ degree $3$ for $g$ near $5?$

$p_3(x)=$

$(c)$ Use the two polynomials that you found $in$ parts $(a)$ and $(b)to$ approximate $g(5\mathrm{.}1).$

With $p_2,g(5\mathrm{.}1)=$

With $p_3,g(5\mathrm{.}1)=$