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: 36

Answer

$-\infty$

Work Step by Step

$\displaystyle \cot x=\frac{\cos x}{\sin t}$ With the unit circle in mind, as $x\rightarrow\pi^{-}$, it is in quadrant II, approaching $\pi.$ In quadrant II, sine is positive, cosine is negative. The numerator is negative, approaching $-1$. The denominator approaches 0, and is positive. $\displaystyle \lim_{x\rightarrow\pi^{-}}\cot x=-\infty$
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