Example $47.1.$ Find $an$ expression for the maximum error when the first $4$ terms $of$ the Maclaurin series for the

function

$f(x)=\frac{1}{1+ax},a$ a positive constant

are used $to$ approximate the function $on$ the interval $0x0\mathrm{.}1.$

What $is$ the largest value $ofaif$ the maximum error must $be$ less than $or$ equal $to{10}^{-8}?$