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

The Following Picture Has The Question That Has Me Troubled Can You Show Me How To Get To The Answer class=

Answer :

Given that:

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

Find the change.

[tex]\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}[/tex]

Find the estimate value.

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

Determine the approximate error.

[tex]\begin{gathered} |\nabla f-df|=|0.0123474175-0.0123743687| \\ =0.0000269512 \\ \approx0.00002 \end{gathered}[/tex]

Option B is correct.