The image contains a mathematical problem involving a function and its behavior as the input approaches infinity. Let's extract and analyze the problem and then provide a solution.

Problem Analysis

The problem seems to ask about the limit of a given function $f(x)$ as $x$ approaches infinity. From the graph:

• The function appears to approach a horizontal asymptote, specifically the line $y = 0$ as $x$ increases.
• The task is to determine the value of this limit.

Solution

From the graph, it is evident that as $x \to \infty$, the function $f(x)$ gets closer and closer to the x-axis, suggesting that the function approaches zero. Thus, the limit of the function as $x \to \infty$ is:

$\lim_{x \to \infty} f(x) = 0$

Would you like more details or have any questions?

Related Questions:

1. What does a horizontal asymptote indicate about a function's behavior?
2. How can you formally prove a limit using algebraic techniques?
3. What are some common functions with horizontal asymptotes?
4. How does the concept of limits apply to real-world scenarios?
5. What is the importance of understanding function behavior at infinity?

Tip:

Always look for asymptotes in a graph, as they provide valuable information about the function's behavior as it approaches extreme values.