Evaluate lim x→∞ f(x) and lim x→−∞ f(x) sing the figure.

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Accepted Answer

Hi everyone, let's take a look at this practice problem dealing with limits. This problem says to determine the value of the limit as X approaches infinity of F of X and the limit as X approaches minus infinity of F of X using the figure. Below the question we're given a graph that has two horizontal asymptotes, one at Y is equal to pi divided by 2, and one at Y is equal to minus pi divided by 2. We also have plotted on the graph, our function Y is equal to FX. We're also given 4 possible choices as our answers. For choice A, we have the limit, as X approaches minus infinity of F of X is equal to minus pi divided by 2, and the limit as X approaches infinity of F of X is equal to pi divided by 2. For choice B, we have the limit as X approaches minus infinity of F of X is equal to pi divided by 2, and the limit as X approaches infinity of F of X is equal to minus pi divided by 2. For choice C, we have the limit as X approaches minus infinity of F of X is equal to minus pi divided by 2, and the limit as X approaches affinity of F of X is equal to minus pi divided by 2. For choice D, we have the limit as x approaches minus affinity of F of X is equal to pi divided by 2, and the limit as x approaches infinity of F of X is equal to pi divided by 2. Now we're asked to calculate the limit as X approaches plus or minus infinity of our function F of X using the figure. And here in the figure we have two horizontal asymptotes. So recall that as X approaches plus or minus infinity, our function F of X needs to approach the value of one of these horizontal asymptotes. So, we're gonna start off by looking at the limit as X approaches minus infinity of our function F of X. So, if I look at my graph, as X approaches minus infinity, Our function F of X is approaching the horizontal asymptote of minus pi divided by 2. So, in this case, our limit as X approaches minus infinity of F of X is going to be equal to minus pi divided by 2. Now, we're now going to look at the limit as X approaches infinity. So, for that limit, we'll have X approaches infinity of F of X. And here, as X approaches infinity, our function F of X is actually approaching the horizontal asymptote at Y is equal to pi divided by 2. That means that our limit as X approaches affinity of F of X is going to be equal to pi divided by 2. So those are the values of the two limits that we were that we were asked to calculate, and we can come down here to our answer choices. And if we look at our answer choices, the correct answer choice corresponds to answer choice A. So I hope that this explanation has been useful, and I'll see you in the next video.

Evaluate lim x→∞ f(x) and lim x→−∞ f(x) sing the figure. <IMAGE>

Key Concepts

Limits at Infinity

Horizontal Asymptotes

Graphical Interpretation

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