Final answer:
Without specific information about the functions f(x), g(x), and h(x), we can only speculate about their limits as x approaches 3 based on given characteristics and general principles. A horizontal line function will have a constant limit, the function with a discontinuity presents uncertainty, and the diverging function likely does not have a finite limit.
Step-by-step explanation:
To find the limits of the functions f(x), g(x), and h(x) as x approaches 3, we first need to know the explicit forms of these functions. Without the specific equations or descriptions of these functions, we cannot compute their limits directly. However, we can draw on some general principles of limits and given information to make observations:
- The limit of f(x) as x approaches 3 is the value that f(x) approaches as x gets arbitrarily close to 3. If f(x) is a continuous function at x = 3, then the limit is simply f(3). Given that f(x) is a horizontal line within a certain interval, if 3 is within this interval, the limit will just be the constant value that f(x) equals everywhere on its domain.
- The limit of g(x) cannot be found without more information, particularly since it has been noted that the function has a discontinuity, which could affect the limit as x approaches 3.
- For the function h(x), we know that it diverges, which means that as x approaches 3, the function does not approach a finite limit. Thus, we can say that the limit does not exist or is infinite, depending on the behavior of the function around x = 3.
For continuous probability functions, such as f(x) mentioned in the context of P(x > 3), the question typically pertains to finding the area under the curve from the point x = 3 to the end of the domain of f(x). This instructs on how to interpret probabilities from the graph of a probability distribution, relevant for understanding limits in statistics.