Consider the following function.

$f(x)=\sqrt[\phantom{2}]{x},a=4,n=2,4x4\mathrm{.}1$

$($a$)$ Approximate $f$ by a Taylor polynomial with degree $n$ at the number $a.$

$T_2(x)=$

$($b$)$ Use Taylor's Inequality to estimate the accuracy of the approximation $f(x)$~~$T_n(x)$ when $x$ lies in the given interval. $($Round your answer to six decimal places.$)$

$|R_2(x)|$