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: 28

Answer

$g(\theta)$ has vertical asymptotes at the values $\theta$ such that $\theta=\dfrac{\pi +2\pi k}{2}$ where $k$ is an integer.

Work Step by Step

$g(\theta)=\dfrac{\tan{\theta}}{\theta}=\dfrac{\sin{\theta}}{\theta\cos{\theta}}.$ Vertical asymptotes occur when the denominator alone is $0\to$ $\theta\cos{\theta}=0\to \cos{\theta}=0$ or $\theta=0.$ $\theta=0$ is rejected since $\sin{0}$ is also $0.$ $\cos{\theta}=0\to\theta=\pi k +\dfrac{\pi}{2}$ where $k$ is an integer.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.