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Let $f$ be a function such that:

$$ \lim \limits_{x \to -5^+} \frac{f(x)-f(-5)}{x+5} =2$$

Which of the following must be true?

I. $f(-5)$ exists
II. $f’(-5)$ exists
III. $f(x)$ is continuous and differentiable at $x=-5$

A

II only.

B

II and III only.

C

I, II, and III.

D

None of the statements are true.

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