University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 2 - Practice Exercises - Page 111: 20


$$\lim_{x\to\pi^-}\csc x=\infty$$

Work Step by Step

$$A=\lim_{x\to\pi^-}\csc x=\lim_{x\to\pi^-}\frac{1}{\sin x}$$ As $x\to\pi^-$, $\sin x$ approaches $0$ from the left, where the values of $\sin x$ are positive. Therefore, as $x\to\pi^-$, $1/\sin x$ will approach $\infty$. $$A=\infty$$
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