Question

Use a linear approximation to estimate the number √9.05 .

Answer 1

you can probably use
\[f(x)=\sqrt{9+x}\] and linearize that one
then use \(x=.05\)

Answer 2

\[f(x)=\sqrt{9+x}\] at \((0,3)\)
\[f'(x)=\frac{1}{2\sqrt{9+x}}\]\[f'(0)=\frac{1}{6}\]

Answer 3

your lineariziation is
\[y=\frac{1}{6}x+3\]

Answer 4

then finish by replacing \(x\) by \(.05\)