164k views
3 votes
What are the limits and values of f(x) as x approaches 2 and 4?

1) lim x → 2- f(x)
2) lim x → 2 f(x)
3) lim x → 2 f(x)
4) f(2)
5) lim x → 4 f(x)
6) f(4)

User Ostoura
by
7.4k points

1 Answer

0 votes

Final answer:

The limits and values of a function as x approaches specific points are examined to determine the function's behavior around those points. For a continuous probability distribution, the area under the probability density function represents the probability between two points.

Step-by-step explanation:

To discuss the limits and values of a function f(x) as x approaches certain points, we need to examine the behavior of the function around those points to determine if a limit exists and what it might be. Without the specific function f(x) provided, we can still discuss the principles involved.

1) The notation lim x → 2- refers to the limit of f(x) as x approaches 2 from the left (negative side).
2) lim x → 2 is the limit as x approaches 2 from either side, provided the limit is the same from both sides.
3) f(2) is the value of the function at x = 2, if it exists.
4) lim x → 4 refers to the limit of f(x) as x approaches 4.
5) f(4) is the value of the function at x = 4.

In the context of continuous probability distribution functions mentioned in the figures and exercises, these concepts help describe the behavior around certain values and calculate probabilities. For example, the probability of a random variable being within a certain range is represented by the area under the probability density function (PDF) between two points.

User Ryan Rinaldi
by
8.0k points