Find the Taylor polynomial $T_2(x)$ for the function $f(x)=2e^{2x}$ at $x=0.$

$($Use symbolic notation and fractions where needed.$)$

$T_2(x)=$

$$

Use a calculator to compute the error at $x=-0\mathrm{.}5.$

$($Use decimal notation. Give your answer to three decimal places.$)$

$|f(x)-T_2(x)|$