Answer
a) 0.0582;
b) Absolute error: $6.9\cdot 10^{-5}$
Work Step by Step
We are given the function $f$ and the Taylor polynomial $p_2$:
$f(x)=\ln (1+x)$
$p_2(x)=x-\dfrac{x^2}{2}$
a) Let $x=0.06$
Compute $p_2(x)$ for $x=0.06$:
$p_2(0.06)=0.06-\dfrac{0.06^2}{2}=0.0582$
b) Use a computer to determine the exact value of $\ln 1.06$:
$\ln 1.06=0.058268908$
Determine the absolute error:
$|\text{exact value}-\text{approximating value}|=|0.058268908-0.0582|=0.000068908=6.9\cdot 10^{-5}$
