THESHADOW

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

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

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

\(=\frac{1}{2\sqrt{6}}\) = 0.20412

At first, I needed help with this confusing math problem about limits, but then I looked at it differently and found the solutions I needed to continue.

1. \(\displaystyle \lim_{x \to 2^{-}}g(x) = \) 4

2. \(\displaystyle \lim_{x \to 2^{+}}g(x) =\) -2

3. \(\displaystyle \lim_{x \to 2}g(x) =\) DNE

4. \(\displaystyle \lim_{x \to 0}g(x) = \) DNE

5. \(\displaystyle g(2) =\) 3