Answer
$$0.001,\ \ \ 0.00101525 ,\ \ \ 0.000015254$$
Work Step by Step
Given $$\frac{1}{\sqrt{98}}-\frac{1}{10} $$
Consider $f(x)= \dfrac{1}{\sqrt{x} }$, $a= 100$, $\Delta x=-2$, since
\begin{align*}
f'(x) &= \frac{-1}{2}x^{-3/2}\\
f'(100)&=-0.0005
\end{align*}
Then the linear approximation is given by
\begin{align*}
\Delta &f \approx f^{\prime}(a) \Delta x\\
&= (-0.0005)(-2)\\
&= 0.001
\end{align*}
and the actual change is given by
\begin{align*}
\Delta f&=f(a+\Delta x)-f(a)\\
&=f(98)-f(100) \\
&\approx 0.00101525
\end{align*}
Hence the error is
$$|0.001-0.00101525|=0.000015254$$
