Difficult# Understand the Nuances of Two-sided Limits

APCALC-XIM4Q1

Let $f$ be a function such that:

$$\lim \limits_{x \to -3^+} \frac{f(x)-f(-3)}{x+3} =\lim \limits_{x \to -3^-} \frac{f(x)-f(-3)}{x+3}$$

Which of the following must be true?

I.$f(-3)$ exists.

II.$f’(-3)$ exists.

III.$f(x)$ is continuous and differentiable at $x=-3$.