$(3$ pts$)14$a$)$ Find the $3$rd degree Taylor polynomial, $T_2(x),$ for the function $f(x)=xlnx$ centered at $x=1$

$(3$ pts$)14$b$)$ Use your Taylor polynomial from part $($a$)$ to estimate the value of $2ln(2)(3$ pts$)14$c$)$ Use your Taylor polynomial from part $($b$)$ to find $T_3(100).$ Briefly explain why this does NOT give a good estimate of $100ln(100)(3$ pts$)14$a$)$ Find the $3$rd degree Taylor polynomial, $T_2(x),$ for the function $f(x)=xlnx$ centered at $x=1$

$(3$ pts$)14$b$)$ Use your Taylor polynomial from part $($a$)$ to estimate the value of $2ln(2)$