Answer
a) $0.86125$;
b) Absolute error: $5.4\cdot 10^{-4}$
Work Step by Step
We are given the function $f$ and the Taylor polynomial $p_2$:
$f(x)=e^{-x}$
$p_2(x)=1-x+\dfrac{x^2}{2}$
a) Let $x=0.15$
Compute $p_2(x)$ for $x=0.15$:
$p_2(0.15)=1-0.15+\dfrac{0.15^2}{2}=0.86125$
b) Use a computer to determine the exact value of $e^{-0.15}$:
$e^{-0.15}=0.86071$
Determine the absolute error:
$|\text{exact value}-\text{approximating value}|=|0.86071-0.86125|=0.00054=5.4\cdot 10^{-4}$
