1. The problem asks to find the limit $$\lim_{x \to 3} \big(h(x) g(x)\big)$$. 2. To find this limit, we need the values of $$h(x)$$ and $$g(x)$$ near $$x=3$$ or their individual limits at $$x=3$$ if they exist. 3. Since the problem only gives the expression and multiple choice answers without explicit functions or values for $$h(x)$$ and $$g(x)$$, we must infer from the choices or additional data (which is not provided). 4. Typically, if $$h(x)$$ and $$g(x)$$ are continuous at $$x=3$$, then $$\lim_{x \to 3} h(x)g(x) = h(3)g(3)$$. Without explicit functions or values, the problem cannot be solved directly here. 5. Since choices are numeric limits: 0, 1, 3, 5, or limit does not exist, the best answer without further data is that the limit does not exist if no function values are known. 6. However, if we assume the problem is complete and expects a choice, and $h(3)g(3)$ is defined and matches one of these values, that value would be the limit. Without more information, the safe assumption is the limit does not exist. Final answer: The limit does not exist.