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If we know for a function $f(x)$ that $f(3)=5$, which of the following must be true in order for $f(x)$ to be continuous at $x=3$?

I. $\mathop {\lim }\limits_{x \to {3^ + }} f(x) = \mathop {\lim }\limits_{x \to {3^ - }} f(x)$
II. $\mathop {\lim }\limits_{x \to 3} f(x) = 5$
III. $\mathop {\lim }\limits_{x \to 5} f(x) = 3$

A

I only.

B

III only.

C

I and II only.

D

I, II, and III.

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