1. The problem asks to estimate the limit $$\lim_{x \to -10} h(x)$$ using the given table of values for $$h(x)$$ near $$x = -10$$. 2. The limit $$\lim_{x \to a} f(x)$$ is the value that $$f(x)$$ approaches as $$x$$ gets closer and closer to $$a$$ from both sides. 3. From the table, as $$x$$ approaches $$-10$$ from the left (values like $$-10.1, -10.01, -10.001$$), $$h(x)$$ values are $$-9.89, -9.47, -9.02$$, which are increasing towards $$-9$$. 4. As $$x$$ approaches $$-10$$ from the right (values like $$-9.999, -9.99, -9.9$$), $$h(x)$$ values are $$-8.01, -8.3, -8.94$$, which are decreasing towards about $$-8.5$$. 5. Since the left-hand limit (approaching $$-9$$) and the right-hand limit (approaching about $$-8.5$$) are not equal, the two-sided limit does not exist. 6. Therefore, the reasonable estimate for $$\lim_{x \to -10} h(x)$$ is that the limit does not exist. Final answer: E. The limit doesn't exist.