1. The problem states: For question 2, the limit $\lim_{x \to a} g(x)$ exists but $g(a)$ is not defined. 2. This means that as $x$ gets closer to $a$, the function values $g(x)$ approach some finite value $L$, i.e., $$\lim_{x \to a} g(x) = L$$ for some real number $L$. 3. However, $g(a)$ is not defined, which means the function does not have a value at $x = a$. 4. This situation is common in cases like removable discontinuities (holes in the graph) where the function approaches a value but is not defined exactly at that point. 5. So, even though $g(a)$ is not defined, the limit can still exist. Answer: $\lim_{x \to a} g(x)$ exists (equals $L$), but $g(a)$ is undefined, indicating a removable discontinuity at $x = a$.