Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.5 The Limit of a Function - 1.5 Exercises: 37

Answer

$-\infty$

Work Step by Step

As $x\rightarrow 2\pi^{-}$, we note that it is positive (close to $ 2\pi$). With the unit circle in mind, $x$ is in quadrant IV, where the sine is negative so $\sin x$ is negative and approaching 0 Cosecant and sine are reciprocal, so as $x\rightarrow 2\pi^{-}$, $\displaystyle \csc x=\frac{1}{\sin x}\rightarrow-\infty$ So, the product ($x\csc x$)$\rightarrow-\infty$
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