The given information specifies:

• $\lim_{x \to 2^+} g(x) = 2$, meaning the right-hand limit of $g(x)$ as $x$ approaches 2 is 2.
• $\lim_{x \to 2^-} g(x) = 3$, meaning the left-hand limit of $g(x)$ as $x$ approaches 2 is 3.
• $g(2)$ is not defined.

Conclusion:

Since the left-hand limit ($3$) and the right-hand limit ($2$) as $x$ approaches 2 are not equal, the overall limit of $g(x)$ as $x \to 2$ does not exist. For a function to have a limit at a point, the left-hand and right-hand limits must be equal.

Additionally, $g(2)$ is not defined, so there is no value of the function at $x = 2$.

Would you like further details on why the limit does not exist in this case?

---

Here are some related questions:

1. What are one-sided limits, and how are they different from two-sided limits?
2. Can a function still be continuous if the left-hand and right-hand limits differ?
3. How can we graphically interpret the information about $g(x)$ near $x = 2$?
4. What does it mean for a function to be undefined at a point, and how does it affect limits?
5. How do we determine the overall limit of a function at a point?

Tip: When checking for limits, always consider both one-sided limits to ensure they match for the overall limit to exist!