University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 4 - Section 4.5 - Indeterminate Forms and L'Hôpital's Rule - Exercises - Page 248: 70



Work Step by Step

Here, $\lim\limits_{x \to 0^{+}} f(x)=\lim\limits_{x \to \dfrac{\pi}{2}^{-}} \dfrac{\cot x}{\csc x}$ This implies that $\lim\limits_{x \to 0^{+}} (\dfrac{cos x/\sin x}{1/\sin x})=\lim\limits_{x \to 0^{+}} \dfrac{\cos x}{\sin x}(\sin x)$ Thus, $\cos (0)=1$
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