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.$\mathop {\lim }\limits_{x \to 5} f(x) = 3$