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

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Let \(f(x) = \sqrt{x} - 7\).

Then \(\displaystyle \lim_{ h \rightarrow 0 } \frac{f(6 + h) - f(6)}{h} = \)

THESHADOW Sep 8, 2022

THESHADOW · Answer 1 · 2022-09-08T04:15:15

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

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

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

\(=\frac{1}{2\sqrt{6}}\) = 0.20412