a$.$ Use the given Taylor polynomial $P_2$ to approximate the given quantity.

b$.$ Compute the absolute error in the approximation assuming the exact value is given by a calculator.

Approximate $ln(1\mathrm{.}09)$ using $f(x)=ln(1x)$ and $p_2(x)=x-\frac{x^2}{2}.$

a$.$ Using the Taylor polynomial $P_2,ln(1\mathrm{.}09)$~~ $$

$($Do not round until the final answer. Then round to four decimal places as needed.$)$