Let $f(x)=\frac{1}{\sqrt[3]{2-x}},$ and $a=1.$

$($a$)(2$ points$)$ Find the degree $2$ Taylor polynomial $P_2$ about $a=1.$

Answer:

$($b$)(2$ points$)$ Use your answer to estimate $f(1\mathrm{.}1).$

$($c$)(3$ points$)$ Find a good upper bound for the error in your estimate