Question

refer to the graph of y = f(x) to the right to describe the behavior of lim f(x). use - ∞ and ∞ where appropriate.

select the correct choice below and fill in any answer boxes in your choice.

a. lim f(x) =

b. the limit does not exist and is neither - ∞ nor ∞.

Explanation:

Step1: Observe the graph as x approaches infinity

As \(x\to\infty\), we look at the right - hand side of the graph to see the long - term behavior of \(y = f(x)\).

Step2: Determine the limit value

From the graph, as \(x\) gets larger and larger (tends to infinity), the function \(y = f(x)\) approaches a horizontal asymptote. The \(y\) - value of the horizontal asymptote is \(y = 0\). So \(\lim_{x\to\infty}f(x)=0\).

Answer:

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