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: 72

Answer

Vertical asymptotes at every integer value of $x.$

Work Step by Step

A function has vertical asymptotes at values that make only the denominator $0$. $f(x)=\csc{\pi x}=\dfrac{1}{\sin{\pi x}}\to \sin{\pi x}=0 \to \pi x=\pi k\to x=k$ where $k$ is any integer.
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