use the table to determine a reasonable estimate for lim(x→3) (2x² - x + 15)/(x³ - 5x - 12)\n2.9…

Explanation:

Step1: Analyze the table values

As $x$ approaches 3 from the left - hand side ($x = 2.9,2.99,2.999$), the values of $f(x)$ are getting closer to 0.5. As $x$ approaches 3 from the right - hand side ($x=3.001,3.01,3.1$), the values of $f(x)$ are also getting closer to 0.5.

Step2: Determine the limit estimate

Since the left - hand limit and the right - hand limit seem to be approaching the same value as $x$ approaches 3, we can estimate the limit.

Answer:

$\frac{1}{2}$