+0  
 
+1
38
1
avatar+136 

Let \(f(x) = \sqrt{x} - 7\).

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

 Sep 8, 2022
 #1
avatar+136 
+2

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

 

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

 

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

 

\(=\frac{1}{2\sqrt{6}}\) = 0.20412

 Sep 8, 2022

6 Online Users