The statement is true.

Here's why:

If the limit of $F(x)$ as $x$ approaches 9 exists, then $F(x)$ could potentially be continuous at $x = 9$. However, for $F(x)$ to be continuous at $x = 9$, three conditions must be met:

1. $F(9)$ must be defined.
2. $\lim_{{x \to 9}} F(x)$ must exist.
3. $\lim_{{x \to 9}} F(x) = F(9)$.

So, the existence of the limit $\lim_{{x \to 9}} F(x)$ means that continuity is possible, but other conditions (like $F(9)$ being defined and equal to the limit) must also be satisfied for $F(x)$ to be continuous at $x = 9$.

Would you like more details or have any questions?

Here are 5 related questions:

1. What are the formal conditions for a function to be continuous at a point?
2. Can a function be continuous if its limit exists but is not equal to its function value at the point?
3. How can we determine the existence of a limit at a point?
4. What is the difference between one-sided and two-sided limits?
5. Can a function have a limit at a point where it is not defined?

Tip: Continuity at a point requires the function's limit at that point to match the function's actual value at that point.