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Calculus / Calculus: Early Transcendentals 9 / Chapter 2.6 / Problem 51

Calculus: Early Transcendentals | 9th Edition | ISBN: 9781337613927 | Authors: Daniel K. Clegg, Saleem Watson, James Stewart

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?Find the horizontal and vertical asymptotes of each curve. You may want to use a

Chapter 2, Problem 51

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QUESTION:

Find the horizontal and vertical asymptotes of each curve. You may want to use a graphing calculator (or computer) to check your work by graphing the curve and estimating the asymptotes.

\(y=\frac{x^{3}-x}{x^{2}-6 x+5}\)

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QUESTION:

Find the horizontal and vertical asymptotes of each curve. You may want to use a graphing calculator (or computer) to check your work by graphing the curve and estimating the asymptotes.

\(y=\frac{x^{3}-x}{x^{2}-6 x+5}\)

ANSWER:

Step 1 of 5

The goal of the exercise is to find horizontal and vertical asymptotes of the given function.

Recall that a function has a vertical asymptote if at some point of the domain function tends to become vertical, that is function starts to approach or .

A rational function has a vertical asymptote whenever its denominator is zero.

The denominator of the given function is .

So we get the denominator is zero at and and thus it follows that the possible vertical asymptotes are and

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