1. **State the problem:** We need to find the limit $$\lim_{x\to 3} \big(h(x)g(x)\big)$$ where functions $h$ and $g$ are given graphically. 2. **Recall the limit product rule:** If $$\lim_{x\to a} h(x) = L$$ and $$\lim_{x\to a} g(x) = M$$ both exist, then $$\lim_{x\to a} h(x)g(x) = LM$$. 3. **Find $$\lim_{x\to 3} h(x)$$:** From the graph description, as $x$ approaches 3, $h(x)$ approaches the value at the open circle at $(3,1)$, so $$\lim_{x\to 3} h(x) = 1$$. 4. **Find $$\lim_{x\to 3} g(x)$$:** From the graph description, as $x$ approaches 3, $g(x)$ approaches the value at the closed circle at $(3,5)$, so $$\lim_{x\to 3} g(x) = 5$$. 5. **Calculate the product limit:** Using the product rule, $$\lim_{x\to 3} h(x)g(x) = \lim_{x\to 3} h(x) \times \lim_{x\to 3} g(x) = 1 \times 5 = 5$$. **Final answer:** $$\boxed{5}$$