 lim
x→2+ g(x) = 2
• lim
x→2− g(x) = 3
• g(2) is not defined

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?

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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!

lim x→2+ g(x) = 2
lim x→2− g(x) = 3
g(2) is not defined

Understand how to solve for limits with one-sided limits at x=2. This problem focuses on key calculus concepts such as limits, right-hand and left-hand limits, and continuity. Suitable for high school students in Grades 10-12.

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