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: 27

Answer

Vertical asymptotes at the values $t$ such that $t=\pi k$ where k is a non-zero integer.

Work Step by Step

$s(t)=\dfrac{t}{\sin{t}}$. Vertical asymptotes occur when the denominator alone is $0\to$ $\sin{t}=0\to t=\pi k$ where k is a non-zero integer. Note: The reason $k=0$ is excluded is because it makes both the numerator and denominator $0.$
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