Let $$\displaystyle v$$ be the function defined above. Which of the following statements about $$\displaystyle v$$ are true?

$$\displaystyle v(x) = \begin{cases} \displaystyle \sqrt{x+6} & \text{if } x < 3 \\ \displaystyle 2x - 3 & \text{if } x \geq 3 \end{cases}$$

I. $$\displaystyle \lim_{x \to 3^-} v(x) = \lim_{x \to 3^+} v(x)$$

II. $$\displaystyle \lim_{x \to 3^-} v'(x) = \lim_{x \to 3^+} v'(x)$$

III. $$\displaystyle v$$ is differentiable at $$x = 3$$.