Answer
a) 0.9624;
b) Absolute error: $1.5\cdot 10^{-4}$
Work Step by Step
We are given the function $f$ and the Taylor polynomial $p_2$:
$f(x)=\dfrac{1}{\sqrt{1+x}}$
$p_2(x)=1-\dfrac{x}{2}+\dfrac{3x^2}{8}$
a) Let $x=0.08$
Compute $p_2(x)$ for $x=0.08$:
$p_2(0.08)=1-\dfrac{0.08}{2}+\dfrac{3(0.08^2)}{8}=0.9624$
b) Use a computer to determine the exact value of $\dfrac{1}{\sqrt{1.08}}$:
$\dfrac{1}{\sqrt{1.08}}=0.962250449$
Determine the absolute error:
$|\text{exact value}-\text{approximating value}|=|0.962250449-0.9624|=0.000149551=1.5\cdot 10^{-4}$
