Let f(x) = sqrt{x} - 7. Then lim {h -> 0} (f(6 + h) - f(6))/h =

\(\lim _{\:h\rightarrow 0\:}\frac{\left(\sqrt{6+h}-7\right)-\left(\sqrt{6}-7\right)}{h}\)

 

\(=\lim _{h\to \:0}\left(\frac{\sqrt{h+6}-\sqrt{6}}{h}\right)\)

 

\(=\lim _{h\to \:0}\left(\frac{1}{\sqrt{h+6}+\sqrt{6}}\right)\)

 

\(=\frac{1}{2\sqrt{6}}\) = 0.20412