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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

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

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.

Harvey Mudd College

Baylor University

Boston College

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this problem One of this tour calculus eighth edition section two point six Explain in your own words the meaning of each of the following party we have the limit is shown. Limited's expert is infinity of f of X is equal to five ah in words. We can explain this limit as the function out be the behavior of the function of as X is piecing Lee larger as it tends towards infinity that this function acts will approach value five but never reached the value five. So again, as we tend towards positive infinity the function f behaves such that it will approach five but never for part b. The limited specs approaches negative infinity of every lex is equal to three. This is similar in that the behavior the function have as X approaches negative infinity. So as we decrease our increase negatively towards negative infinity, the function itself will three but never reach three

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