The correct answer is $$\infty$$. As $$x$$ approaches -4 from the left, the values of $$g(x)$$ are increasing without bound. As $$x$$ approaches -4 from the right, the values of $$g(x)$$ are also increasing without bound. Since both sides approach positive infinity, the limit is considered to be $$\infty$$. Choice A is one of the data points. Choice D is incorrect because the behavior from both sides is the same (approaching $$\infty$$).

The correct answer is -0.5. The limit as $$x \to -\infty$$ describes the end behavior of the function as $$x$$ decreases without bound. The table shows that as $$x$$ becomes more negative, the values of $$h(x)$$ get closer to -0.5. Choice C is the first value in the table. Choice B is a common limit value but not supported by the data. Choice D is incorrect as the values are approaching a single number.

The correct answer is 6. From the table, as $$x \to -3$$, $$f(x) \to 12$$ and $$g(x) \to 2$$. Using the quotient property of limits, $$\lim_{x \to -3} \frac{f(x)}{g(x)} = \frac{\lim_{x \to -3} f(x)}{\lim_{x \to -3} g(x)} = \frac{12}{2} = 6$$. Choice B is the sum of the limits. Choice C is the sum of the function values at x=-3 (if they were given). Choice D is incorrect because the individual limits exist and the denominator's limit is not zero.

The correct answer is -4. The notation $$x \to 3^+$$ indicates the limit as $$x$$ approaches 3 from the right side (values greater than 3). The table shows that for $$x$$ values of 3.001, 3.01, and 3.1, the values of $$h(x)$$ are approaching -4. Choice A is the left-hand limit. Choice C is the value $$x$$ is approaching. Choice D is incorrect because the one-sided limit exists.

The correct answer is 4. The expression in the limit is the definition of the derivative of $$f$$ at $$x=2$$, i.e., $$f'(2)$$. The table directly provides values of this difference quotient as $$h$$ approaches 0 from the left and the right. As $$h \to 0^-$$, the quotient approaches 4. As $$h \to 0^+$$, the quotient approaches 4. Since both one-sided limits are equal, the limit is 4. Choice C is the value of $$f(2)$$.

The correct answer is 5. From the table, as $$x \to 4$$, $$f(x) \to 7$$ and $$g(x) \to -2$$. Using the sum property of limits, $$\lim_{x \to 4} (f(x) + g(x)) = \lim_{x \to 4} f(x) + \lim_{x \to 4} g(x) = 7 + (-2) = 5$$. Choice B is the difference of the limits. Choice C is the sum of the first values in the table. Choice D is incorrect because both individual limits exist.

The correct answer is 5. As $$x$$ approaches 2 from the left ($$x=1.9, 1.99, 1.999$$), $$f(x)$$ approaches 5. As $$x$$ approaches 2 from the right ($$x=2.001, 2.01, 2.1$$), $$f(x)$$ also approaches 5. Since the left-hand and right-hand limits are equal, the limit is 5. The value $$f(2)=7$$ is irrelevant to the value of the limit. Choice B is the value of the function at $$x=2$$, not the limit. Choice C is a single value from the table, not the limit. Choice D is incorrect because the left and right limits both approach 5.

The correct answer is 9. The notation $$x \to -1^-$$ indicates the limit as $$x$$ approaches -1 from the left side (values less than -1). The table shows that for $$x$$ values of -1.1, -1.01, and -1.001, the values of $$g(x)$$ are approaching 9. Choice A is the value of the function at $$x=-1$$. Choice B is the right-hand limit, not the left-hand limit. Choice D is incorrect because the one-sided limit exists.

The correct answer is 3. The limit as $$x \to \infty$$ describes the end behavior of the function as $$x$$ increases without bound. The table shows that as $$x$$ gets larger, the values of $$f(x)$$ get closer and closer to 3. Choice A is a common limit value but not supported by the data. Choice C is the first value in the table. Choice D is incorrect as the values are approaching a single number.

The correct answer is -14. From the table, as $$x \to 4$$, $$f(x) \to 7$$ and $$g(x) \to -2$$. Using the product property of limits, $$\lim_{x \to 4} (f(x) \cdot g(x)) = (\lim_{x \to 4} f(x)) \cdot(\lim_{x \to 4} g(x)) = 7 \cdot(-2) = -14$$. Choice B is the sum of the limits. Choice C is the product of the first values in the table. Choice D is incorrect because both individual limits exist.