1. The problem asks us to estimate the limit $$\lim_{x \to 6} f(x)$$ given the table of values for $f(x)$ near $x=6$. 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 6 from the left (5.98, 5.99), $f(x)$ values are 4.19 and 4.18. - As $x$ approaches 6 from the right (6.01, 6.02, 6.03), $f(x)$ values are 4.18, 4.19, and 4.2. 4. Notice that at $x=6$, $f(6) = 0.2$, which is very different from the values near 6. 5. The limit depends on the values approaching 6, not the value at 6 itself. 6. Since the values of $f(x)$ near 6 from both sides are close to about 4.18 to 4.2, the reasonable estimate for the limit is approximately 4.18. 7. Among the answer choices, 4.17 (option B) is the closest reasonable estimate. **Final answer:** $$\lim_{x \to 6} f(x) \approx 4.17$$