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 - 1.4 Exercises - Page 80: 44


$f(x)$ has two vertical asymptotes (non-removable discontinuity) at $x=2$ and $x=-2.$

Work Step by Step

$f(x)=\dfrac{x}{x^2-4}=\dfrac{x}{(x-2)(x+2)}\to x\ne2$ and $x\ne-2$ Hence since the denominator is zero at both values, the function has non-removable discontinuities at $x=2$ and $x=-2.$
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