Answer
a) $0.7264$;
b) Absolute error: $0.01462$
Work Step by Step
We are given the function $f$ and the Taylor polynomial $p_2$:
$f(x)=\dfrac{1}{(1+x)^3}$
$p_2(x)=1-3x+6x^2$
a) Let $x=0.12$
Compute $p_2(x)$ for $x=0.12$:
$p_2(0.12)=1-3(0.12)+6(0.12^2)=0.7264$
b) Use a computer to determine the exact value of $\dfrac{1}{1.12^3}$:
$\dfrac{1}{1.12^3}= 0.711780248$
Determine the absolute error:
$|\text{exact value}-\text{approximating value}|=|0.711780248-0.7264|=0.014619752\approx 0.01462$
