1. Let's first clarify the problem: We are considering a function with a point at $x=2$ that is an open circle (not included in the function). We want to know if this changes any of the limits at or around $x=2$. 2. Recall the definition of limits: The limit of a function $f(x)$ as $x$ approaches a value $a$ depends on the behavior of $f(x)$ near $a$, but not necessarily the value of $f(a)$ itself. 3. Important rule: The limit $\lim_{x \to a} f(x)$ exists if and only if the left-hand limit $\lim_{x \to a^-} f(x)$ and the right-hand limit $\lim_{x \to a^+} f(x)$ both exist and are equal. 4. The value of the function at $x=2$ (whether the point is open or closed) does not affect the limit $\lim_{x \to 2} f(x)$. 5. However, the value of the function at $x=2$ does affect the actual function value $f(2)$, but not the limit. 6. Therefore, having an open point at $x=2$ does not change the left-hand limit, right-hand limit, or the overall limit at $x=2$. Final answer: No, making the point at $x=2$ open does not change any of the limits at $x=2$.