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