Calculate the following limit or specify that it does not exist.

${\lim }_{v\to 0}\frac{\sqrt{36+v}-6}{v}$

Evaluate the limit of the function $f\left(x\right)=\frac{3x+1}{\cos x}$ as $x\to 0^{+}$.

Find the limit:

$\underset{x\to 4^{+}}{\lim }\frac{3}{\sqrt{x(x-4)}}$

Use the following theorem to evaluate $\underset{x\to 0}{\lim }\frac{\tan 14x}{x}$:

$\underset{x\to 0}{\lim }\frac{\sin x}{x}=1$