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AP® Calculus AB-BC

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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 $x=-3$

A

II only.

B

I and II only.

C

I, II, and III.

D

None of the statements are true.