Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.5 Exercises: 23

Answer

No vertical asymptotes.

Work Step by Step

$f(x)=\dfrac{x^2-2x-15}{x^3-5x^2+x-5}=\dfrac{(x-5)(x+3)}{(x-5)(x^2+1)}=\dfrac{x+3}{x^2+1}.$ Vertical asymptotes occur when the denominator alone is $0\to$ $x^2+1=0\to x^2=-1$ which has no real solution, hence the function has no vertical asymptotes.
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