$f(x)=xsin(x),a=0,n=4,-0\mathrm{.}7x0\mathrm{.}7$

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

$T_4(x)=$

$($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 four decimal places.$)$

$|R_4(x)|$

$($c$)$ Check your result in part $($b$)$ by graphing $|R_n(x)|.$

$(1)$