Answer
$$0.98,\ \ 0.980392,\ \ 3.922\times 10^{-4}$$
Work Step by Step
Given $$\frac{1}{1.02}$$
Consider $f(x)=\frac{1}{x}, a=1,$ and $\Delta x=0.02$, since
\begin{align*}
f^{\prime}(x)&=\frac{-1}{x^2} \\
f^{\prime}(1)&=-1
\end{align*}
Then the linear approximation is given by
\begin{align*}
L(x)&=f^{\prime}(a)(x-a)+f(a)\\
&= -(x-1)+ 1=2-x\\
L(1.02)&\approx 2-1.02= 0.98
\end{align*}
By using a calculator, $\frac{1}{1.02} =0.980392$ and the error in the linear approximation is$$
|0.980392- 0.98|=3.922\times 10^{-4}
$$
