Question

The following picture has the question that has me troubled can you show me how to get to the answer

Answer 1

Given that:

$f(x)=\sqrt[]{x},x_0=8,dx=0.07$

Find the change.

$\begin{gathered} \nabla f=f(8+\text{0}.07)-f(8) \\ =f(8.07)-f(8) \\ =\sqrt[]{8.07}-\sqrt[]{8} \\ =0.0123474175 \end{gathered}$

Find the estimate value.

$\begin{gathered} df=\frac{1}{2\sqrt[]{8}}\cdot0.07 \\ =0.0123743687 \end{gathered}$

Determine the approximate error.

$\begin{gathered} |\nabla f-df|=|0.0123474175-0.0123743687| \\ =0.0000269512 \\ \approx0.00002 \end{gathered}$

Option B is correct.