calculus - If the function is continuous at some point, then is it necessary that limit should exist at that point?

If the function is continuous at some point, then is it necessary that limit should exists at that point?

Like in case of $\sqrt{x}$, its continuous at $x=0$, but limit doesn't exist as left hand limit is not defined.

But it appears meaningless to say that function is continuous at some point, but limit doesn't exist at that point.

Any inputs?