Science:Math Exam Resources/Courses/MATH110/April 2016/Question 05 (c)
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Question 05 (c)
(c) Find all the vertical and horizontal asymptotes of , if they exist.
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To find vertical asymptotes, use the fact that when is the ratio of two polynomials, the only candidates for vertical asymptotes are the values of for which the denominator is zero.
To find horizontal asymptotes, determine the behaviour of when approaches to .
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Since the denominator is zero exactly when , it is the only candidate for the vertical asymptote.
As approaches to , the numerator approaches to , while the denominator approaches 0. This gives
In other words, has exactly one vertical asymptote, which is .
On the other hand, we have
It follows that it has as its horizontal asymptote.
Answer, the asymptotes are: .