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: 25

Answer

$f(x)$ has a vertical asymptote at every integer value of $x.$

Work Step by Step

$f(x)=\csc{\pi x}=\dfrac{1}{\sin{\pi x}}$ Vertical asymptotes occur when the denominator alone is $0\to$ $\sin{\pi x}=0\to \pi x=\pi k\to x=k$ where $k$ is an integer.
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