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Explain in your own words the meaning of each of the following.

(a) $ \displaystyle \lim_{x \to \infty} f(x) = 5 $

(b) $ \displaystyle \lim_{x \to - \infty} f(x) = 3 $

(a) As $x$ becomes large, the values of $f(x)$ approach 5

(b) As $x$ becomes large negative, the values of $f(x)$ approach 3

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Pio H.

February 22, 2021

Can the graph of y=f(x) intersect a vertical asymptote? can it intersect a horizontal asymptote? illustrate by sketching graphs.

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

for this problem, we are to explain the meaning of each of the following statement. The first one is the limit of F of X as X approaches infinity equals five, and The other one is the limit of the function. As X approaches negative infinity equals three. Now, for the first one, since X approaches infinity, then it tells us that we are moving far to the right and we're looking at the value the function varied approaches to and since this is equal to five, then as we move far right, the value of the function approaches to five. Because X approaches an infinite value, The value of F of X can never equal five. It will only approach it. And so we can say that the function Has a horizontal sm so that y equal to five. Now for the 2nd 1, since we're approaching negative infinity, then we're moving far to the left. And so as you move far to the left, the value of the function approaches 23 And because X approaches negative infinity, Then the value of F of X can never equal to three. It will only approach it. Hence we can say that F of X has a horizontal essent. Oh, dad, Why equal to 3?