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 - Review Exercises: 52

Answer

$f(x)$ has two irremovable discontinuities (vertical asymptotes) at $x=3$ and $x=-3.$

Work Step by Step

$f(x)=\dfrac{1}{x^2-9}=\dfrac{1}{(x-3)(x+3)};x\ne3, x\ne-3$ When $x=3$ or $x=-3,$ the denominator is $0$, indicating the presence of a vertical asymptote at both points. These discontinuities are not removable.
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