Find the second Taylor polynomial T$2($x$)$ for the function f$($x$)=$cos$($x$)$ based at b$=$

$6$

$.$

T$2($x$)=$

Let a be a positive real number and let J be the closed interval

$6$

$$a$,$

$6$

$+$a

$.$ Use the Quadratic Approximation Error Bound to verify that

$|$f$($x$)$T$2($x$)|$

a$33!$

for all x in J$.$

Use this error bound to find a value of a so that

$|$f$($x$)$T$2($x$)|0\mathrm{.}01$

for all x in J$.($Round your answer to six decimal places.$)$

a$=$